information theoretic determination of minimax rates of convergence we present some general results determining minimax bounds on statistical risk for density estimation based on certain information theoretic considerations these bounds depend only on metric entropy conditions and are used to identify the minimax rates of convergence

blind separation of positive sources by globally convergent gradient search the instantaneous noise free linear mixing model in independent component analysis is largely a solved problem under the usual assumption of independent nongaussian sources and full column rank mixing matrix however with some prior information on the sources like positivity new analysis and perhaps simplified solution methods may yet become possible in this letter we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded which means that they have a nonzero pdf in the region of zero it can be shown that in this case the solution method is basically very simple an orthogonal rotation of the whitened observation vector into nonnegative outputs will give a positive permutation of the original sources we propose a cost function whose minimum coincides with nonnegativity and derive the gradient algorithm under the whitening constraint under which the separating matrix is orthogonal we further prove that in the stiefel manifold of orthogonal matrices the cost function is a lyapunov function for the matrix gradient flow implying global convergence thus this algorithm is guaranteed to find the nonnegative well grounded independent sources the analysis is complemented by a numerical simulation which illustrates the algorithm

efficient estimation for the proportional hazards model with interval censoring the maximum likelihood estimator mle for the proportional hazards model with case 1 interval censored data is studied it is shown that the mle for the regression parameter is asymptotically normal with n convergence rate and achieves the information bound even though the mle for the baseline cumulative hazard function only converges at n 1 3 rate estimation of the asymptotic variance matrix for the mle of the regression parameter is also considered to prove our main results we also establish a general theorem showing that the mle of the finite dimensional parameter in a class of semiparametric models is asymptotically efficient even though the mle of the infinite dimensional parameter converges at a rate slower than n the results are iliustrated by applying them to a data set from a tumorigenicity study

learning overcomplete representations in an overcomplete basis the number of basis vectors is greater than the dimensionality of the input and the representation of an input is not a unique combination of basis vectors overcomplete representations have been advocated because they have greater robustness in the presence of noise can be sparser and can have greater flexibility in matching structure in the data overcomplete codes have also been proposed as a model of some of the response properties of neurons in primary visual cortex previous work has focused on finding the best representation of a signal using a fixed overcomplete basis or dictionary we present an algorithm for learning an overcomplete basis by viewing it as probabilistic model of the observed data we show that overcomplete bases can yield a better approximation of the underlying statistical distribution of the data and can thus lead to greater coding efficiency this can be viewed as a generalization of the technique of independent component analysis and provides a method for bayesian reconstruction of signals in the presence of noise and for blind source separation when there are more sources than mixtures

blind source separation with nonlinear autocorrelation and non gaussianity blind source separation bss is a problem that is often encountered in many applications such as biomedical signal processing and analysis speech and image processing wireless telecommunication systems data mining sonar radar enhancement etc one often solves the bss problem by using the statistical properties of original sources e g non gaussianity or time structure information nevertheless real life mixtures are likely to contain both non gaussianity and time structure information sources rendering the algorithms using only one statistical property fail in this paper we address the bss problem when source signals have non gaussianity and temporal structure with nonlinear autocorrelation based on the two statistical characteristics of sources we develop an objective function maximizing the objective function we propose a gradient ascent source separation algorithm furthermore we give some mathematical properties for the algorithm computer simulations for sources with square temporal autocorrelation and non gaussianity illustrate the efficiency of the proposed approach

implicit dynamic analysis using an isogeometric reissner mindlin shell formulation summary in isogeometric analysis identical basis functions are used for geometrical representation and analysis in this work non uniform rational basis splines basis functions are applied in an isoparametric approach an isogeometric reissner mindlin shell formulation for implicit dynamic calculations using the galerkin method is presented a consistent as well as a lumped matrix formulation is implemented the suitability of the developed shell formulation for natural frequency analysis is demonstrated by a numerical example in a second set of examples transient problems of plane and curved geometries undergoing large deformations in combination with nonlinear material behavior are investigated via a zero thickness stress algorithm for arbitrary material models a j2 plasticity constitutive law is implemented in the numerical examples the effectiveness robustness and superior accuracy of a continuous interpolation method of the shell director vector is compared with experimental results and alternative numerical approaches copyright 2016 john wiley sons ltd

global risk bounds and adaptation in univariate convex regression we consider the problem of nonparametric estimation of a convex regression function phi 0 we study the risk of the least squares estimator lse under the natural squared error loss we show that the risk is always bounded from above by n 4 5 modulo logarithmic factors while being much smaller when phi 0 is well approximable by a piecewise affine convex function with not too many affine pieces in which case the risk is at most 1 n up to logarithmic factors on the other hand when phi 0 has curvature we show that no estimator can have risk smaller than a constant multiple of n 4 5 in a very strong sense by proving a local minimax lower bound we also study the case of model misspecification where we show that the lse exhibits the same global behavior provided the loss is measured from the closest convex projection of the true regression function in the process of deriving our risk bounds we prove new results for the metric entropy of local neighborhoods of the space of univariate convex functions these results which may be of independent interest demonstrate the non uniform nature of the space of univariate convex functions in sharp contrast to classical function spaces based on smoothness constraints

rates of convergence for bayes and maximum likelihood estimation for mixture of normal densities we study the rates of convergence of the maximum likelihood estimator mle and posterior distribution in density estimation problems where the densities are location or location scale mixtures of normal distributions with the scale parameter lying between two positive numbers the true density is also assumed to lie in this class with the true mixing distribution either compactly supported or having sub gaussian tails we obtain bounds for hellinger bracketing entropies for this class and from these bounds we deduce the convergence rates of sieve mles in hellinger distance the rate turns out to be log n n where k 1 is a constant that depends on the type of mixtures and the choice of the sieve next we consider a dirichlet mixture of normals as a prior on the unknown density we estimate the prior probability of a certain kullback leibler type neighborhood and then invoke a general theorem that computes the posterior convergence rate in terms the growth rate of the hellinger entropy and the concentration rate of the prior the posterior distribution is also seen to converge at the rate log n n in where k now depends on the tail behavior of the base measure of the dirichlet process

current status data with competing risks consistency and rates of convergence of the mle we study nonparametric estimation of the sub distribution functions for current status data with competing risks our main interest is in the nonparametric maximum likelihood estimator mle and for comparison we also consider a simpler naive estimator both types of estimators were studied by jewell van der laan and henneman biometrika 2003 90 183 197 but little was known about their large sample properties we have started to fill this gap by proving that the estimators are consistent and converge globally and locally at rate n1 3 we also show that this local rate of convergence is optimal in a minimax sense the proof of the local rate of convergence of the mle uses new methods and relies on a rate result for the sum of the mles of the sub distribution functions which holds uniformly on a fixed neighborhood of a point our results are used in groeneboom maathuis and wellner ann statist 2008 36 1064 1089 to obtain the local limiting distributions of the estimators

on estimating a density using hellinger distance and some other strange facts on s interesse ici aux possibles vitesses d estimation d une densite a support compact dans m sous des hypotheses de regularite lorsque la perte est mesuree par le carre de la distance de hellinger on regardera aussi le cas connu des normes mathbb l q pour 1 q 2 et le risque est le risque minimax sur la famille on donne une methode generale permettant de traiter les problemes dans le cadre de la theorie de l approximation sous des conditions concernant l entropie metrique et l e capacite des familles a estimer les rapports entre regularite et entropie metrique etant bien connus nous pourrons aussi traiter les cas classiques et d autres qui le sont moins sous des conditions de bornes inferieures les vitesses sont celles observees pour la norme mathbb l q mais elles different dans le cas general on montre aussi que les restrictions sur la compacite du support ou la regularite sont indispensables et que leur absence mene a l impossibilite d obtenir une estimation raisonnable en ce sens que n importe quelle suite d estimateurs sera arbitrairement mauvaise en un point au moins un resultat analogue est vrai sous des conditions de regularite

blind source separation by nonstationarity of variance a cumulant based approach blind separation of source signals usually relies either on the nongaussianity of the signals or on their linear autocorrelations a third approach was introduced by matsuoka et al 1995 who showed that source separation can be performed by using the nonstationarity of the signals in particular the nonstationarity of their variances in this paper we show how to interpret the nonstationarity due to a smoothly changing variance in terms of higher order cross cumulants this is based on the time correlation of the squares energies of the signals and leads to a simple optimization criterion using this criterion we construct a fixed point algorithm that is computationally very efficient

subdivision surfaces a new paradigm for thin shell finite element analysis we develop a new paradigm for thin shell finite element analysis based on the use of subdivision surfaces for i describing the geometry of the shell in its undeformed configuration and ii generating smooth interpolated displacement fields possessing bounded energy within the strict framework of the kirchhoff love theory of thin shells the particular subdivision strategy adopted here is loop s scheme with extensions such as required to account for creases and displacement boundary conditions the displacement fields obtained by subdivision are h2 and consequently have a finite kirchhoff love energy the resulting finite elements contain three nodes and element integrals are computed by a one point quadrature the displacement field of the shell is interpolated from nodal displacements only in particular no nodal rotations are used in the interpolation the interpolation scheme induced by subdivision is non local i e the displacement field over one element depend on the nodal displacements of the element nodes and all nodes of immediately neighbouring elements however the use of subdivision surfaces ensures that all the local displacement fields thus constructed combine conformingly to define one single limit surface numerical tests including the belytschko et al 10 obstacle course of benchmark problems demonstrate the high accuracy and optimal convergence of the method

renyi divergence and kullback leibler divergence renyi divergence is related to renyi entropy much like kullback leibler divergence is related to shannon s entropy and comes up in many settings it was introduced by renyi as a measure of information that satisfies almost the same axioms as kullback leibler divergence and depends on a parameter that is called its order in particular the renyi divergence of order 1 equals the kullback leibler divergence we review and extend the most important properties of renyi divergence and kullback leibler divergence including convexity continuity limits of sigma algebras and the relation of the special order 0 to the gaussian dichotomy and contiguity we also show how to generalize the pythagorean inequality to orders different from 1 and we extend the known equivalence between channel capacity and minimax redundancy to continuous channel inputs for all orders and present several other minimax results

a fixed point algorithm for blind source separation with nonlinear autocorrelation this paper addresses blind source separation bss problem when source signals have the temporal structure with nonlinear autocorrelation using the temporal characteristics of sources we develop an objective function based on the nonlinear autocorrelation of sources maximizing the objective function we propose a fixed point source separation algorithm furthermore we give some mathematical properties of the algorithm computer simulations for sources with square temporal autocorrelation and the real world applications in the analysis of the magnetoencephalographic recordings meg illustrate the efficiency of the proposed approach thus the presented bss algorithm which is based on the nonlinear measure of temporal autocorrelation provides a novel statistical property to perform bss

on bayesian consistency we consider a sequence of posterior distributions based on a data dependent prior which we shall refer to as a pseudoposterior distribution and establish simple conditions under which the sequence is hellinger consistent it is shown how investigations into these pseudo posteriors assist with the understanding of some true posterior distributions including polya trees the infinite dimensional exponential family and mixture models

isogeometric kirchhoff love shell formulations for general hyperelastic materials abstract we present formulations for compressible and incompressible hyperelastic thin shells which can use general 3d constitutive models the necessary plane stress condition is enforced analytically for incompressible materials and iteratively for compressible materials the thickness stretch is statically condensed and the shell kinematics are completely described by the first and second fundamental forms of the midsurface we use c 1 continuous isogeometric discretizations to build the numerical models numerical tests including structural dynamics simulations of a bioprosthetic heart valve show the good performance and applicability of the presented methods

rates of convergence for minimum contrast estimators we shall present here a general study of minimum contrast estimators in a nonparametric setting although our results are also valid in the classical parametric case for independent observations these estimators include many of the most popular estimators in various situations such as maximum likelihood estimators least squares and other estimators of the regression function estimators for mixture models or deconvolution the main theorem relates the rate of convergence of those estimators to the entropy structure of the space of parameters optimal rates depending on entropy conditions are already known at least for some of the models involved and they agree with what we get for minimum contrast estimators as long as the entropy counts are not too large but under some circumstances large entropies or changes in the entropy structure due to local perturbations the resulting the rates are only suboptimal counterexamples are constructed which show that the phenomenon is real for non parametric maximum likelihood or regression this proves that under purely metric assumptions our theorem is optimal and that minimum contrast estimators happen to be suboptimal

asymptotics of the discrete log concave maximum likelihood estimator and related applications the assumption of log concavity is a flexible and appealing non parametric shape constraint in distribution modelling in this work we study the log concave maximum likelihood estimator of a probability mass function we show that the maximum likelihood estimator is strongly consistent and we derive its pointwise asymptotic theory under both the well specified and misspecified settings our asymptotic results are used to calculate confidence intervals for the true log concave probability mass function both the maximum likelihood estimator and the associated confidence intervals may be easily computed by using the r package logcondiscr we illustrate our theoretical results by using recent data from the h1n1 pandemic in ontario canada

a discussion of stress rates in finite deformation problems abstract it has recently been shown that the finite elastic plastic solution of the simple shear problem exhibits an oscillatory stress response when kinematic hardening is employed while the solution for isotropic hardening gives a monotonically increasing stress this paper analyzes this response on the basis of continuum mechanical descriptions of the problem three objective stress rates are recalled and spatial descriptions of plasticity at finite deformation are reviewed for the usual generalization of the infinitesimal theory as well as a theory based on an invariant measure of true stress in light of the equations for the evolution of the yield surface the hypoelastic solution to the simple shear problem for each of the three stress rates is presented it is shown that the use of the jaumann rate in the generalization of the infinitesimal theory leads to an oscillation in the evolution of the yield surface in simple shear which is explained on the basis of the hypoelastic solution an alternative theory which makes use of the polar decomposition predicts a monotonically increasing shear stress

an isogeometric continuum shell element for non linear analysis an isogeometric continuum shell formulation is proposed in which nurbs basis functions are used to construct the reference surface of the shell through the thickness behavior is interpolated using a higher order b spline which is in contrast to the standard continuum shell solid like shell formulation where a linear lagrange shape function is typically used in the thickness direction the present formulation yields a complete isogeometric representation of the continuum shell the shell element is implemented in a standard finite element code using bezier extraction which facilitates numerical integration on the reference surface of the shell through the thickness integration is done using a connectivity array which determines the support of a b spline basis function over an element the formulation has been verified using different linear and geometrically non linear examples the ability of the formulation in modelling buckling of static delaminations in composite materials is also demonstrated

probability inequalities for empirical processes and a law of the iterated logarithm given a class f of functions on x we can view vn as a stochastic process indexed by f and consider limit theorems for this process to prove such theorems it is often helpful to have bounds on the tail of the r v sup w i n f i see for example dudley 1978 kuelbs and dudley 1980 dudley and phillip 1983 or gine and zinn 1983 our main question of interest is for what classes f can best possible bounds be obtained so first we must ask what are these best possible bounds of course

estimation of a k monotone density limit distribution theory and the spline connection we study the asymptotic behavior of the maximum likelihood and least squares estimators of a kmonotone density g0 at a fixed point x0 when k 2 we find that the jth derivative of the estima tors at x0 converges at the rate n k j 2k 1 for j 0 k 1 the limiting distribution depends on an almost surely uniquely de fined stochastic process hk that stays above below the k fold in tegral of brownian motion plus a deterministic drift when k is even odd both the mle and lse are known to be splines of degree k 1 with simple knots establishing the order of the random gap n n where n denote two successive knots is a key ingredient of the proof of the main results we show that this gap problem can be solved if a conjecture about the upper bound on the error in a particular hermite interpolation via odd degree splines holds

donsker type theorems for nonparametric maximum likelihood estimators let mathcal p be a nonparametric probability model consisting of smooth probability densities and let hat p n be the corresponding maximum likelihood estimator based on n independent observations each distributed according to the law mathbb p with hat mathbb p n denoting the measure induced by the density hat p n define the stochastic process hat nu n f longmapsto sqrt n int fd hat mathbb p n mathbb p where f ranges over some function class mathcal f we give a general condition for donsker classes mathcal f implying that the stochastic process hat nu n is asymptotically equivalent to the empirical process in the space ell infty mathcal f of bounded functions on mathcal f this implies in particular that hat nu n converges in law in ell infty mathcal f to a mean zero gaussian process we verify the general condition for a large family of donsker classes mathcal f we give a number of applications convergence of the probability measure hat mathbb p n to mathbb p at rate sqrt n in certain metrics metrizing the topology of weak star convergence a unified treatment of convergence rates of the mle in a continuous scale of sobolev norms sqrt n efficient estimation of nonlinear functionals defined on mathcal p limit theorems at rate sqrt n for the maximum likelihood estimator of the convolution product mathbb p ast p

concentration inequalities and asymptotic results for ratio type empirical processes let be a class of measurable functions on a measurable space s mathcal s with values in 0 1 and let pn n 1 i 1n xi be the empirical measure based on an i i d sample x1 xn from a probability distribution p on s mathcal s we study the behavior of suprema of the following type sup r n textless sigma p f leq delta n frac p n f pf phi sigma p f where pf var1 2pf and is a continuous strictly increasing function with 0 0 using talagrand s concentration inequality for empirical processes we establish concentration inequalities for such suprema and use them to derive several results about their asymptotic behavior expressing the conditions in terms of expectations of localized suprema of empirical processes we also prove new bounds for expected values of sup norms of empirical processes in terms of the largest pf and the l2 p norm of the envelope of the function class which are especially suited for estimating localized suprema with this technique we extend to function classes most of the known results on ratio type suprema of empirical processes including some of alexander s results for vc classes of sets we also consider applications of these results to several important problems in nonparametric statistics and in learning theory including general excess risk bounds in empirical risk minimization and their versions for l2 regression and classification and ratio type bounds for margin distributions in classification

hellinger consistency of certain nonparametric maximum likelihood estimators consider a class mathscr p p theta theta in theta of probability measures on a measurable space mathscr x mathscr a dominated by a sigma finite measure mu let f theta dp theta d mu theta in theta and let theta n be a maximum likelihood estimator based on n independent observations from p theta 0 theta 0 in theta we use results from empirical process theory to obtain convergence for the hellinger distance h f hat theta n f theta 0 under certain entropy conditions on the class of densities f theta theta in theta the examples we present are a model with interval censored observations smooth densities monotone densities and convolution models in most examples the convexity of the class of densities is of special importance

exponential inequalities for martingales with application to maximum likelihood estimation for counting processes we obtain an exponential probability inequality for martingales and a uniform probability inequality for the process gdn where n is a counting process and where g varies within a class of predictable functions g for the latter we use techniques from empirical process theory the uniform inequality is shown to hold under certain entropy conditions on g as an application we consider rates of convergence for nonparametric maximum likelihood estimators for counting processes a similar result for discrete time observations is also presented

treatment of reissner mindlin shells with kinks without the need for drilling rotation stabilization in an isogeometric framework this work presents a framework for the computation of complex geometries containing intersections of multiple patches with reissner mindlin shell elements the main objective is to provide an isogeometric finite element implementation which neither requires drilling rotation stabilization nor user interaction to quantify the number of rotational degrees of freedom for every node for this purpose the following set of methods is presented control points with corresponding physical location are assigned to one common node for the finite element solution a nodal basis system in every control point is defined which ensures an exact interpolation of the director vector throughout the whole domain a distinction criterion for the automatic quantification of rotational degrees of freedom for every node is presented an isogeometric reissner mindlin shell formulation is enhanced to handle geometries with kinks and allowing for arbitrary intersections of patches the parametrization of adjacent patches along the interface has to be conforming the shell formulation is derived from the continuum theory and uses a rotational update scheme for the current director vector the nonlinear kinematic allows the computation of large deformations and large rotations two concepts for the description of rotations are presented the first one uses an interpolation which is commonly used in standard lagrange based shell element formulations the second scheme uses a more elaborate concept proposed by the authors in prior work which increases the accuracy for arbitrary curved geometries numerical examples show the high accuracy and robustness of both concepts the applicability of the proposed framework is demonstrated

a nonnegative pca algorithm for independent component analysis we consider the task of independent component analysis when the independent sources are known to be nonnegative and well grounded so that they have a nonzero probability density function pdf in the region of zero we propose the use of a nonnegative principal component analysis nonnegative pca algorithm which is a special case of the nonlinear pca algorithm but with a rectification nonlinearity and we conjecture that this algorithm will find such nonnegative well grounded independent sources under reasonable initial conditions while the algorithm has proved difficult to analyze in the general case we give some analytical results that are consistent with this conjecture and some numerical simulations that illustrate its operation

the nonparametric maximum likelihood estimator in a class of doubly censored current status data models with application to partner studies summary the california partners study is an ongoing investigation of heterosexual hiv transmission in partners of infected index cases padian et al 1987 shiboski jewell 1990 we consider a nonparametric maximum likelihood estimator of the distribution of the time t the partner is exposed to an infected index partner until infection based on doubly censored current status data we provide a modified iterative weighted pool adjacent violator algorithm for computation of the nonparametric maximum likelihood estimator and show that the estimator converges at rate n 3 in addition we propose confidence intervals for smooth functionals of the distribution of t simulations show good performance of the algorithm and confidence intervals we apply our methodology to the california partners study and discuss the implications of our results for doubly censored current status data models with other known distributions of the origin

hybrid linear and nonlinear complexity pursuit for blind source separation blind source separation bss is an increasingly popular data analysis technique with many applications several methods for bss using the statistical properties of original sources have been proposed for a famous case non gaussianity this leads to independent component analysis ica in this paper we propose a hybrid bss method based on linear and nonlinear complexity pursuit which combines three statistical properties of source signals non gaussianity linear predictability and nonlinear predictability a gradient learning algorithm is presented by minimizing a loss function simulations verify the efficient implementation of the proposed method

blind source separation using temporal predictability a measure of temporal predictability is defined and used to separate linear mixtures of signals given any set of statistically independent source signals it is conjectured here that a linear mixture of those signals has the following property the temporal predictability of any signal mixture is less than or equal to that of any of its component source signals it is shown that this property can be used to recover source signals from a set of linear mixtures of those signals by finding an un mixing matrix that maximizes a measure of temporal predictability for each recovered signal this matrix is obtained as the solution to a generalized eigenvalue problem such problems have scaling characteristics of o n3 where n is the number of signal mixtures in contrast to independent component analysis the temporal predictability method requires minimal assumptions regarding the probability density functions of source signals it is demonstrated that the method can separate signal mixtures in which each mixture is a linear combination of source signals with supergaussian subgaussian and gaussian probability density functions and on mixtures of voices and music

on profile likelihood abstract we show that semiparametric profile likelihoods where the nuisance parameter has been profiled out behave like ordinary likelihoods in that they have a quadratic expansion in this expansion the score function and the fisher information are replaced by the efficient score function and efficient fisher information the expansion may be used among others to prove the asymptotic normality of the maximum likelihood estimator to derive the asymptotic chi squared distribution of the log likelihood ratio statistic and to prove the consistency of the observed information as an estimator of the inverse of the asymptotic variance

isogeometric kirchhoff love shell formulation for elasto plasticity abstract an isogeometric thin shell formulation allowing for large strain plastic deformation is presented a stress based approach is adopted which means that the constitutive equations are evaluated at different integration points through the thickness allowing the use of general 3d material models the plane stress constraint is satisfied by iteratively updating the thickness stretch at the integration points the deformation of the shell structure is completely described by the deformation of its midsurface and furthermore the formulation is rotation free which means that the discrete shell model involves only three degrees of freedom several numerical benchmark examples with comparison to fully 3d solid simulations confirm the accuracy and efficiency of the proposed formulation

blended isogeometric shells abstract we propose a new isogeometric shell formulation that blends kirchhoff love theory with reissner mindlin theory this enables us to reduce the size of equation systems by eliminating rotational degrees of freedom while simultaneously providing a general and effective treatment of kinematic constraints engendered by shell intersections folds boundary conditions the merging of nurbs patches etc we illustrate the blended theory s performance on a series of test problems

efficient matrix computation for tensor product isogeometric analysis the use of sum factorization abstract in this paper we discuss the use of the sum factorization for the calculation of the integrals arising in galerkin isogeometric analysis while introducing very little change in an isogeometric code based on element by element quadrature and assembling the sum factorization approach taking advantage of the tensor product structure of splines or nurbs shape functions significantly reduces the quadrature computational cost

blind separation of instantaneous mixtures of nonstationary sources most source separation algorithms are based on a model of stationary sources however it is a simple matter to take advantage of possible nonstationarities of the sources to achieve separation this paper develops novel approaches in this direction based on the principles of maximum likelihood and minimum mutual information these principles are exploited by efficient algorithms in both the off line case via a new joint diagonalization procedure and in the on line case via a newton like procedure some experiments showing the good performance of our algorithms and evidencing an interesting feature of our methods are presented their ability to achieve a kind of super efficiency the paper concludes with a discussion contrasting separating methods for non gaussian and nonstationary models and emphasizing that as a matter of fact what makes the algorithms work is strictly speaking not the nonstationarity itself but rather the property that each realization of the source signals has a time varying envelope

fast nonlinear autocorrelation algorithm for source separation independent component analysis ica and blind source separation bss methods have been used for pattern recognition problems it is well known that ica and bss depend on the statistical properties of original sources or components such as non gaussianity in the paper using a statistical property nonlinear autocorrelation and maximizing the nonlinear autocorrelation of source signals we propose a fast fixed point algorithm for bss we study its convergence property and show that its convergence speed is at least quadratic simulations by the artificial signals and the real world applications verify the efficient implementation of the proposed method

estimating a unimodal distribution from interval censored data in this article we consider three nonparametric maximum likelihood estimators based on mixed case interval censored data apart from the unrestricted estimator we consider estimators under the assumption that the underlying distribution function of event times is concave or unimodal characterizations of the estimates are derived and algorithms are proposed for their computation the estimators are shown to be asymptotically consistent and the benefits of additional constraints are illustrated through simulations finally the estimators are used as an ingredient in a nonparametric comparison of two samples

law of the iterated logarithm for set indexed partial sum processes with finite variance is relatively compact in the uniform topology and the set of limit points is the set of functions which are absolutely continuous and whose derivatives have l 2 norm less than or equal to 1 using skorokhod embedding strassen showed that random walks also obeyed a functional lil and that the usual lil as well as many other interesting results could be obtained as a consequence the extension of strassen s results to brownian motion indexed by points in and to partial sum processes indexed by points in ir was done by pyke 7 and wichura 9 respectively for a brownian motion indexed by a large collection d of sets the functional law was proved by bass and pyke 2 and then a type of skorokhod embedding was used to extend this for partial sum processes however if h 5 is the log entropy of d defined in sect 2 it was necessary that h 6 0 moreover the sets in d had to have uniformly smooth boundaries morrow and philipp 6j were able to wea

theory and numerical analysis of shells undergoing large elastic strains abstract a non linear bending theory of rubber like shells undergoing large elastic strains is proposed the theory is based on a relaxed normality hypothesis and the incompressibility condition using series expansion in the normal direction and applying some estimation technique a consistent first approximation and a simplest approximation to the elastic strain energy of the shell are constructed lagrangian displacement shell equations are derived and the incremental shell deformation is considered the numerical results presented for one and two dimensional large strain shell problems confirm the accuracy and efficiency of the proposed shell theory

a nitsche type formulation and comparison of the most common domain decomposition methods in isogeometric analysis this paper provides a detailed elaboration and assessment of the most common domain decomposition methods for their application in isogeometric analysis the methods comprise a penalty approach lagrange multiplier methods and a nitsche type method for the nitsche method a new stabilized formulation is developed in the context of isogeometric analysis to guarantee coercivity all these methods are investigated on problems of linear elasticity and eigenfrequency analysis in 2d in particular focus is put on non uniform rational b spline patches which join nonconformingly along their common interface thus the application of isogeometric analysis is extended to multi patches which can have an arbitrary parametrization on the adjacent edges moreover it has been shown that the unique properties provided by isogeometric analysis that is high order functions and smoothness across the element boundaries carry over for the analysis of multiple domains copyright 2013 john wiley sons ltd

parametric estimation finite sample theory the paper aims at reconsidering the famous le cam lan theory the main features of the approach which make it different from the classical one are as follows 1 the study is nonasymptotic that is the sample size is fixed and does not tend to infinity 2 the parametric assumption is possibly misspecified and the underlying data distribution can lie beyond the given parametric family these two features enable to bridge the gap between parametric and nonparametric theory and to build a unified framework for statistical estimation the main results include large deviation bounds for the quasi maximum likelihood and the local quadratic bracketing of the log likelihood process the latter yields a number of important corollaries for statistical inference concentration confidence and risk bounds expansion of the maximum likelihood estimate etc all these corollaries are stated in a nonclassical way admitting a model misspecification and finite samples however the classical asymptotic results including the efficiency bounds can be easily derived as corollaries of the obtained nonasymptotic statements at the same time the new bracketing device works well in the situations with large or growing parameter dimension in which the classical parametric theory fails the general results are illustrated for the i i d setup as well as for generalized linear and median estimation the results apply for any dimension of the parameter space and provide a quantitative lower bound on the sample size yielding the root n accuracy

discussion local rademacher complexities and oracle inequalities in risk minimization in this magnificent paper professor koltchinskii offers general and powerful performance bounds for empirical risk minimization a fundamental principle of statistical learning theory since the elegant pioneering work of vapnik and chervonenkis in the early 1970s various such bounds have been known that relate the performance of empirical risk minimizers to combinatorial and geometrical features of the class over which the minimization is performed this area of research has been a rich source of motivation and a major field of applications of empirical process theory the appearance of advanced concentration inequalities in the 1990s primarily thanks to talagrand s influential work provoked major advances in both empirical process theory and statistical learning theory and led to a much deeper understanding of some of the basic phenomena in the discussed paper professor koltchinskii develops a powerful new methodology iterative localization which with the help of concentration inequalities is able to explain most of the recent results and go significantly beyond them in many cases the main motivation behind professor koltchinskii s paper is based on classical problems of statistical learning theory such as binary classification and regression in which given a sample xi y i i 1 n of independent and identically distributed pairs of random variables where the xi take their values in some feature space x and the yi are say real valued the goal is to find a function f x r whose risk defined in terms of the expected value of an appropriately chosen loss function is as small as possible in the remaining part of this discussion we point out how the performance bounds of professor koltchinskii s paper can be used to study a seemingly different model motivated by nonparametric ranking problems which has received increasing attention both in the statistical and machine learning literature indeed in several applications such as the search engine problem or credit risk screening the goal is to learn how to rank or to score observations rather than just classify them in this case performance measures involve pairs of observations as can be seen for instance with the auc area under an roc curve criterion in this

fast and robust fixed point algorithms for independent component analysis independent component analysis ica is a statistical method for transforming an observed multidimensional random vector into components that are statistically as independent from each other as possible we use a combination of two different approaches for linear ica comon s information theoretic approach and the projection pursuit approach using maximum entropy approximations of differential entropy we introduce a family of new contrast functions for ica these contrast functions enable both the estimation of the whole decomposition by minimizing mutual information and estimation of individual independent components as projection pursuit directions the statistical properties of the estimators based on such contrast functions are analyzed under the assumption of the linear mixture model and it is shown how to choose contrast functions that are robust and or of minimum variance finally we introduce simple fixed point algorithms for practical optimization of the contrast functions

complexity pursuit separating interesting components from time series a generalization of projection pursuit for time series that is signals with time structure is introduced the goal is to find projections of time series that have interesting structure defined using criteria related to kolmogoroff complexity or coding length interesting signals are those that can be coded with a short code length we derive a simple approximation of coding length that takes into account both the nongaussianity and the autocorrelations of the time series also we derive a simple algorithm for its approximative optimization the resulting method is closely related to blind separation of nongaussian time dependent source signals

analysis of sparse representation and blind source separation in this letter we analyze a two stage cluster then l1 optimization approach for sparse representation of a data matrix which is also a promising approach for blind source separation bss in which fewer sensors than sources are present first sparse representation factorization of a data matrix is discussed for a given overcomplete basis matrix the corresponding sparse solution coefficient matrix with minimum l1 norm is unique with probability one which can be obtained using a standard linear programming algorithm the equivalence of the l1 norm solution and the l0 norm solution is also analyzed according to a probabilistic framework if the obtained l1 norm solution is sufficiently sparse then it is equal to the l0 norm solution with a high probability furthermore the l1 norm solution is robust to noise but the l0 norm solution is not showing that the l1 norm is a good sparsity measure these results can be used as a recoverability analysis of bss as discussed the basis matrix in this article is estimated using a clustering algorithm followed by normalization in which the matrix columns are the cluster centers of normalized data column vectors zibulevsky pearlmutter boll and kisilev 2000 used this kind of two stage approach in underdetermined bss our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed domain and with the case in which the source number is unknown it is also robust to additive noise and estimation error in the mixing matrix finally four simulation examples and an eeg data analysis example are presented to illustrate the algorithm s utility and demonstrate its performance

a new rotation free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries abstract this paper presents a general non linear computational formulation for rotation free thin shells based on isogeometric finite elements it is a displacement based formulation that admits general material models the formulation allows for a wide range of constitutive laws including both shell models that are extracted from existing 3d continua using numerical integration and those that are directly formulated in 2d manifold form like the koiter canham and helfrich models further a unified approach to enforce the g 1 continuity between patches fix the angle between surface folds enforce symmetry conditions and prescribe rotational dirichlet boundary conditions is presented using penalty and lagrange multiplier methods the formulation is fully described in the natural curvilinear coordinate system of the finite element description which facilitates an efficient computational implementation it contains existing isogeometric thin shell formulations as special cases several classical numerical benchmark examples are considered to demonstrate the robustness and accuracy of the proposed formulation the presented constitutive models in particular the simple mixed koiter model that does not require any thickness integration show excellent performance even for large deformations

the glivenko cantelli problem we give a new type of characterization of the glivenko cantelli classes in the case of a class mathscr l of sets the characterization is closely related to the configuration that the sets of mathscr l can have it allows one to decide simply whether a given class is a glivenko cantelli class the characterization is based on a new measure theoretic analysis of sets of measurable functions this analysis also gives an approximation theorem for glivenko cantelli classes sharpenings of the vapnik cervonenkis criteria and the value of the asymptotic discrepancy for classes that are not glivenko cantelli an application is given to the law of large numbers in a banach space for functions that need not be random variables

an efficient model reduction method for buckling analyses of thin shells based on iga abstract an efficient reduced basis method is proposed for buckling analyses of thin shells subject to large deformations and strains the thin shells are modeled with the classical kirchhoff love kinematics under the framework of iga isogeometric analysis which makes it possible to satisfy the requirement of c 1 continuity the analytically defined geometry of thin shells can be exactly represented by the nurbs non uniform rational b splines basis functions in addition the critical buckling point can be better pin pointed due to the exact geometric description for efficient structural analyses a simplified rom reduced order model is presented by combining the koiter perturbation technique and the finite element method fem alternative perturbation forces based on nonlinear eigenvalue analyses are also proposed embedding three strategies including arc length control accompanying eigenvalue analysis and mode injection into the analysis procedure the proposed method is extended to be applicable to nonlinear buckling analyses furthermore imperfection sensitivity analyses can be conveniently performed with the proposed method finally the effectiveness and efficiency of the proposed method are validated via three benchmark problems

a simplified kirchhoff love large deformation model for elastic shells and its effective isogeometric formulation abstract isogeometric kirchhoff love elements have received an increasing attention in geometrically nonlinear analysis of elastic shells nevertheless some difficulties still remain among the others the highly nonlinear expression of the strain measure which leads to a complicated and costly computation of the discrete operators and the existence of locking which prevents the use of coarse meshes for slender shells and low order nurbs are key issues that need to be addressed in this work exploiting the hypothesis of small membrane strains we propose a simplified strain measure with a third order polynomial dependence on the displacement variables which allows an efficient evaluation of the discrete quantities numerical results show practically no difference to the original model even for very large displacements and composite structures patch wise reduced integrations are then investigated to deal with membrane locking in large deformation problems an optimal integration scheme for third order c 2 nurbs in terms of accuracy and efficiency is identified finally the recently proposed newton method with mixed integration points is used for the solution of the discrete nonlinear equations with a great reduction of the iterative burden with respect to the standard newton scheme

a blind source separation technique using second order statistics separation of sources consists of recovering a set of signals of which only instantaneous linear mixtures are observed in many situations no a priori information on the mixing matrix is available the linear mixture should be blindly processed this typically occurs in narrowband array processing applications when the array manifold is unknown or distorted this paper introduces a new source separation technique exploiting the time coherence of the source signals in contrast with other previously reported techniques the proposed approach relies only on stationary second order statistics that are based on a joint diagonalization of a set of covariance matrices asymptotic performance analysis of this method is carried out some numerical simulations are provided to illustrate the effectiveness of the proposed method

equivariant adaptive source separation source separation consists of recovering a set of independent signals when only mixtures with unknown coefficients are observed this paper introduces a class of adaptive algorithms for source separation that implements an adaptive version of equivariant estimation and is henceforth called equivariant adaptive separation via independence easi the easi algorithms are based on the idea of serial updating this specific form of matrix updates systematically yields algorithms with a simple structure for both real and complex mixtures most importantly the performance of an easi algorithm does not depend on the mixing matrix in particular convergence rates stability conditions and interference rejection levels depend only on the normalized distributions of the source signals closed form expressions of these quantities are given via an asymptotic performance analysis the theme of equivariance is stressed throughout the paper the source separation problem has an underlying multiplicative structure the parameter space forms a matrix multiplicative group we explore the favorable consequences of this fact on implementation performance and optimization of easi algorithms

the consistency of posterior distributions in nonparametric problems we give conditions that guarantee that the posterior probability of every hellinger neighborhood of the true distribution tends to 1 almost surely the conditions are 1 a requirement that the prior not put high mass near distributions with very rough densities and 2 a requirement that the prior put positive mass in kullback leibler neighborhoods of the true distribution the results are based on the idea of approximating the set of distributions with a finite dimensional set of distributions with sufficiently small hellinger bracketing metric entropy we apply the results to some examples

mutual information metric entropy and cumulative relative entropy risk assume p theta theta epsilon theta is a set of probability distributions with a common dominating measure on a complete separable metric space y a state theta epsilon theta is chosen by nature a statistician obtains n independent observations y 1 dots y n from y distributed according to p theta for each time t between 1 and n based on the observations y 1 dots y t 1 the statistician produces an estimated distribution hat p t for p theta and suffers a loss l p theta hat p t the cumulative risk for the statistician is the average total loss up to time n of special interest in information theory data compression mathematical finance computational learning theory and statistical mechanics is the special case when the loss l p theta hat p t is the relative entropy between the true distribution p theta and the estimated distribution hat p t here the cumulative bayes risk from time 1 to n is the mutual information between the random parameter theta and the observations y 1 dots y n new bounds on this mutual information are given in terms of the laplace transform of the hellinger distance between pairs of distributions indexed by parameters in theta from these bounds on the cumulative minimax risk are given in terms of the metric entropy of theta with respect to the hellinger distance the assumptions required for these bounds are very general and do not depend on the choice of the dominating measure they apply to both finite and infinite dimensional theta they apply in some cases where y is infinite dimensional in some cases where y is not compact in some cases where the distributions are not smooth and in some parametric cases where asymptotic normality of the posterior distribution fails

estimation of a convex function characterizations and asymptotic theory we study nonparametric estimation of convexregression and density functions by methods of least squares in the regression and density cases and maximum likelihood in the density estimation case we provide characterizations of these estimators prove that they are consistent and establish their asymptotic distributions at a fixed point of positive curvature of the functions estimated the asymptotic distribution theory relies on the existence of an invelope function for integrated two sided brownian motion t 4 which is established in a companion paper by groeneboom jongbloed and wellner

a new constrained fixed point algorithm for ordering independent components independent component analysis ica aims to recover a set of unknown mutually independent components ics from their observed mixtures without knowledge of the mixing coefficients in the classical ica model there exists ics indeterminacy on permutation and dilation constrained ica is one of methods for solving this problem through introducing constraints into the classical ica model in this paper we first present a new constrained ica model which composed of three parts a maximum likelihood criterion as an objective function statistical measures as inequality constraints and the normalization of demixing matrix as equality constraints next we incorporate the new fixed point newfp algorithm into this constrained ica model to construct a new constrained fixed point algorithm computation simulations on synthesized signals and speech signals demonstrate that this combination both can eliminate ics indeterminacy to a certain extent and can provide better performance moreover comparison results with the existing algorithm verify the efficiency of our new algorithm furthermore and show that it is more simple to implement than the existing algorithm due to its advantage of not using the learning rate finally this new algorithm is also applied for the real world fetal ecg data experiment results further indicate the efficiency of the new constrained fixed point algorithm

the central limit theorem and the law of iterated logarithm for empirical processes under local conditions a clt and a lil are proved under weak l2 gaussian bracketing conditions weaker than the usual ones these results have wide applicability and in particular provide an improvement of the jain marcus central limit theorem for c s valued random variables

bayesian mode regression using mixtures of triangular densities abstract bayesian semiparametric models for mean and median regressions abound but a void for mode regressions exists we fill this gap by nonparametrically modeling the error distribution in such regressions that entails constructing prior distributions on densities which exhibit flexibility while fixing the mode at 0 such priors exist when constraining the mean and median but to our knowledge there is none for the mode our solution with mixtures of triangular distributions results in a conditionally conjugate prior on the space of unimodal untruncated convex densities consistency properties of the resulting modal estimators are studied followed by simulated and real data illustrations

global rates of convergence of the mles of log concave and s concave densities we establish global rates of convergence for the maximum likelihood estimators mles of log concave and s concave densities on the main finding is that the rate of convergence of the mle in the hellinger metric is no worse than n 2 5 when 1 s where s 0 corresponds to the log concave case we also show that the mle does not exist for the classes of s concave densities with s 1

isogeometric collocation for the reissner mindlin shell problem abstract we present an isogeometric collocation formulation for the reissner mindlin shell problem after recalling the necessary basics on differential geometry and the shell governing equations we show that the standard approach of expressing the equilibrium equations in terms of the primal variables is not a suitable way for shells due to the complexity of the underlying equations we then propose an alternative approach based on a stepwise formulation and show its numerical implementation within an isogeometric collocation framework the formulation is tested successfully on a set of benchmark examples which comprise important aspects like locking and boundary layers these test show that locking effects can be conveniently avoided by using high polynomial degrees an accompanying study on the computational time also confirms that high polynomial degrees are preferable in terms of computational efficiency

blind source separation by sparse decomposition in a signal dictionary the blind source separation problem is to extract the underlying source signals from a set of linear mixtures where the mixing matrix is unknown this situation is common in acoustics radio medical signal and image processing hyperspectral imaging and other areas we suggest a two stage separation process a priori selection of a possibly overcomplete signal dictionary for instance a wavelet frame or a learned dictionary in which the sources are assumed to be sparsely representable followed by unmixing the sources by exploiting the their sparse representability we consider the general case of more sources than mixtures but also derive a more efficient algorithm in the case of a nonovercomplete dictionary and an equal numbers of sources and mixtures experiments with artificial signals and musical sounds demonstrate significantly better separation than other known techniques

isogeometric shell analysis with nurbs compatible subdivision surfaces we present a discretisation of kirchhoff love thin shells based on a subdivision algorithm that generalises nurbs to arbitrary topology the isogeometric framework combines the advantages of both subdivision and nurbs enabling higher degree analysis on watertight meshes of arbitrary geometry including conic sections because multiple knots are supported it is possible to benefit from symmetries in the geometry for a more efficient subdivision based analysis the use of the new subdivision algorithm is an improvement to the flexibility of current isogeometric analysis approaches and allows new use cases

rotation free isogeometric analysis of an arbitrarily curved plane bernoulli euler beam abstract the present study elucidates linear static analysis for plane beam structures using the isogeometric approach a novel methodology for rotation free analysis of an arbitrarily curved bernoulli euler beam in the convective frame of reference is derived in detail the full degeneration of a 3d continuum beam to a 1d line has been presented and a fully applicable isogeometric finite element has been obtained the driving force behind developing the present research has been the derivation of the nurbs based isogeometric analysis which will enable an elegant formulation of the plane bernoulli euler beams being a function only of the global rectangular cartesian coordinates the verification and accuracy of the research are obtained via a thorough comparison between theory finite element analyses and relevant examples from literature an excellent agreement of results is achieved and usefulness for academic and practical purposes alike are proved the effects of the hpk refinements are illuminated and it is observed that the convergences for the most variables and refinement techniques are not monotonic a special attention is paid to the influence of the product of maximum curvature and thickness of beam on the accuracy of the solution the limits of applicability of the present approach are defined for a few specific types of analyses the derived formulation is geometrically exact and appropriate for the analysis of strongly curved bernoulli euler beams

isogeometric reissner mindlin shell analysis with exactly calculated director vectors abstract an isogeometric reissner mindlin shell derived from the continuum theory is presented the geometry is described by nurbs surfaces the kinematic description of the employed shell theory requires the interpolation of the director vector and of a local basis system hence the definition of nodal basis systems at the control points is necessary for the proposed formulation the control points are in general not located on the shell reference surface and thus several choices for the nodal values are possible the proposed new method uses the higher continuity of the geometrical description to calculate nodal basis system and director vectors which lead to geometrical exact interpolated values thereof thus the initial director vector coincides with the normal vector even for the coarsest mesh in addition to that a more accurate interpolation of the current director and its variation is proposed instead of the interpolation of nodal director vectors the new approach interpolates nodal rotations account is taken for the discrepancy between interpolated basis systems and the individual nodal basis systems with an additional transformation the exact evaluation of the initial director vector along with the interpolation of the nodal rotations lead to a shell formulation which yields precise results even for coarse meshes the convergence behavior is shown to be correct for k refinement allowing the use of coarse meshes with high orders of nurbs basis functions this is potentially advantageous for applications with high numerical effort per integration point the geometrically nonlinear formulation accounts for large rotations the consistent tangent matrix is derived various standard benchmark examples show the superior accuracy of the presented shell formulation a new benchmark designed to test the convergence behavior for free form surfaces is presented despite the higher numerical effort per integration point the improved accuracy yields considerable savings in computation cost for a predefined error bound

an information maximization approach to blind separation and blind deconvolution we derive a new self organizing learning algorithm that maximizes the information transferred in a network of nonlinear units the algorithm does not assume any knowledge of the input distributions and is defined here for the zero noise limit under these conditions information maximization has extra properties not found in the linear case linsker 1989 the nonlinearities in the transfer function are able to pick up higher order moments of the input distributions and perform something akin to true redundancy reduction between units in the output representation this enables the network to separate statistically independent components in the inputs a higher order generalization of principal components analysis we apply the network to the source separation or cocktail party problem successfully separating unknown mixtures of up to 10 speakers we also show that a variant on the network architecture is able to perform blind deconvolution cancellation of unknown echoes and reverberation in a speech signal finally we derive dependencies of information transfer on time delays we suggest that information maximization provides a unifying framework for problems in blind signal processing

subdivision shells with exact boundary control and non manifold geometry we introduce several new extensions to subdivision shells that provide an improved level of shape control over shell boundaries and facilitate the analysis of shells with non smooth and non manifold joints to this end extended subdivision schemes are used that enable to relax the continuity of the limit surface along prescribed crease edges and to create surfaces with prescribed limit positions and normals furthermore shells with boundaries in the form of conic sections such as circles or parabolas are represented with rational subdivision schemes which are defined in analogy to rational b splines in terms of implementation the difference between the introduced and conventional subdivision schemes is restricted to the use of modified subdivision stencils close to the mentioned geometric features hence the resulting subdivision surface is in most parts of the domain identical to standard smooth subdivision surfaces the particular subdivision scheme used in this paper constitutes an improved version of the original loop s scheme and is as such based on triangular meshes as in the original subdivision shells surfaces created with the modified scheme are used for interpolating the reference and deformed shell configurations at the integration points the subdivision surface is evaluated using a newly developed discrete parameterization approach in the resulting finite elements the only degrees of freedom are the mid surface displacements of the nodes and additional lagrange parameters for enforcing normal constraints the versatility of the newly developed elements is demonstrated with a number of geometrically nonlinear shell examples copyright 2011 john wiley sons ltd

an extended isogeometric thin shell analysis based on kirchhoff love theory abstract an extended isogeometric element formulation xiga for analysis of through the thickness cracks in thin shell structures is developed the discretization is based on non uniform rational b splines nurbs the proposed xiga formulation can reproduce the singular field near the crack tip and the discontinuities across the crack it is based on the kirchhoff love theory where c 1 continuity of the displacement field is required this condition is satisfied by the nurbs basis functions hence the formulation eliminates the need of rotational degrees of freedom or the discretization of the director field facilitating the enrichment strategy the performance and validity of the formulation is tested by several benchmark examples

an asymptotic property of model selection criteria probability models are estimated by use of penalized log likelihood criteria related to akaike 1973 information criterion aic and minimum description length mdl the accuracies of the density estimators are shown to be related to the tradeoff between three terms the accuracy of approximation the model dimension and the descriptive complexity of the model classes the asymptotic risk is determined under conditions on the penalty term and is shown to be minimax optimal for some cases as an application we show that the optimal rate of convergence is simultaneously achieved for log densities in sobolev spaces w sub 2 sup s u without knowing the smoothness parameter s and norm parameter u in advance applications to neural network models and sparse density function estimation are also provided

convex models mle and misspecification we analyze the asymptotic behavior of maximum likelihood estimators mle in convex dominated models when the true distribution generating the independent data does not necessarily belong to the model inspired by the hellinger distance and its properties we introduce a family of divergences contrast functions which allow a unified treatment of well and misspecified convex models convergence and rates of convergence of the mle with respect to our divergences are obtained from inequalities satisfied by these divergences and results from empirical process theory uniform laws of large numbers and maximal inequalities as a particular case we recover existing results for hellinger convergence of mle in well specified convex models four examples are considered mixtures of discrete distributions monotone densities decreasing failure rate distributions and a finite dimensional parametric model

asymptotic normality of statistics based on the convex minorants of empirical distribution functions let f be the uniform empirical distribution function write fn for the least concave majorant of f and let an denote the corresponding density it is shown that n fl fn t 1 2 dt is asymptotically standard normal when centered at log n and normalized by 3 log n 1i2 a similar result is obtained in the 2 sample case in which fn is replaced by the slope of the convex minorant of fm fm hn1

convergence rates for density estimation with bernstein polynomials mixture models for density estimation provide a very useful set up for the bayesian or the maximum likelihood approach for a density on the unit interval mixtures of beta densities form a flexible model the class of bernstein densities is a much smaller subclass of the beta mixtures defined by bernstein polynomials which can approximate any continuous density a bernstein polynomial prior is obtained by putting a prior distribution on the class of bernstein densities the posterior distribution of a bernstein polynomial prior is consistent under very general conditions in this article we present some results on the rate of convergence of the posterior distribution if the underlying distribution generating the data is itself a bernstein density then we show that the posterior distribution converges at nearly parametric rate log n sqrt n for the hellinger distance if the true density is not of the bernstein type we show that the posterior converges at a rate n 1 3 log n 5 6 provided that the true density is twice differentiable and bounded away from 0 similar rates are also obtained for sieve maximum likelihood estimates these rates are inferior to the pointwise convergence rate of a kernel type estimator we show that the bayesian bootstrap method gives a proxy for the posterior distribution and has a convergence rate at par with that of the kernel estimator

risk bounds in isotonic regression nonasymptotic risk bounds are provided for maximum likelihood type isotonic estimators of an unknown nondecreasing regression function with general average loss at design points these bounds are optimal up to scale constants and they imply uniform n 1 3 consistency of the ell p risk for unknown regression functions of uniformly bounded variation under mild assumptions on the joint probability distribution of the data with possibly dependent observations

efficient isogeometric nurbs based solid shell elements mixed formulation and b method abstract in this work solid shell nurbs elements are developed in order to address static problems of slender structures under small perturbations a single layer of elements is considered through the thickness of the shell and the degree of approximation in that direction is chosen to be equal to two a full 3d constitutive relation is assumed the objective is to obtain highly accurate low degree elements to be used in coarse meshes in order to do that we propose a mixed method from which we derive a b projection to deal with locking the main idea is to modify the interpolation of the average stresses and strains through the thickness more precisely we develop two finite elements the first element which is based on the mixed method or equivalently on the b projection is extremely accurate but leads to a fully populated global stiffness matrix to improve the efficiency the second element uses a local least squares type procedure to define a new b projection leading to a sparse global stiffness matrix the quality and efficiency of the methods are assessed through several usual test cases and by comparison with other published techniques

weak dirichlet boundary conditions for trimmed thin isogeometric shells computer aided design based nurbs surfaces form the basis of isogeometric shell analysis which exploits the smoothness and higher continuity properties of nurbs to derive a suitable analysis model in an isoparametric sense equipped with higher order approximation capabilities the used nurbs functions focus increasingly on rotation free shell elements which are considered to be difficult in the traditional finite element framework the rotation free formulation of shell elements is elegant and efficient but demands special care to enforce reliably essential translational and rotational boundary conditions which is even more challenging in the case of trimmed boundaries as common in cad models we propose a nitsche based extension of the kirchhoff love theory to enforce weakly essential boundary conditions of the shell we apply our method to trimmed and untrimmed nurbs structures and illustrate a good performance of the method with benchmark test models and a shell model from engineering practice with an extension of the formulation to a weak enforcement of coupling constraints we are able to handle cad derived trimmed multi patch nurbs models for thin shell structures

a simple algorithm for obtaining nearly optimal quadrature rules for nurbs based isogeometric analysis we develop new quadrature rules for isogeometric analysis based on the solution of a local nonlinear problem a simple and robust algorithm is developed to determine the rules which are exact for important b spline spaces of uniform and geometrically stretched knot spacings we consider both periodic and open knot vector configurations and illustrate the efficiency of the rules on selected boundary value problems we find that the rules are almost optimally efficient but much easier to obtain than optimal rules which require the solution of global nonlinear problems that are often ill posed

three dimensional extension of non linear shell formulation based on the enhanced assumed strain concept conventional shell formulations such as 3 or 5 parameter theories or even 6 parameter theories including the thickness change as extra parameter require a condensation of the constitutive law in order to avoid a significant error due to the assumption of a linear displacement field across the thickness this means that the normal stress in thickness direction has to either vanish or be constant in general these extra constraints cannot be satisfied explicitly or they lead to elaborate strain expressions the main objective of the present study is to introduce directly a complete 3 d constitutive law without modification therefore a 7 parameter theory is utilized which includes a linear varying thickness stretch as extra variable allowing also large strain effects