high breakdown point and high efficiency robust estimates for regression a class of robust estimates for the linear model is introduced these estimates called mm estimates have simultaneously the following properties i they are highly efficient when the errors have a normal distribution and ii their breakdown point is 0 5 the mm estimates are defined by a three stage procedure in the first stage an initial regression estimate is computed which is consistent robust and with high breakdown point but not necessarily efficient in the second stage an m estimate of the errors scale is computed using residuals based on the initial estimate finally in the third stage an m estimate of the regression parameters based on a proper redescending psi function is computed consistency and asymptotical normality of the mm estimates assuming random carriers are proved a convergent iterative numerical algorithm is given finally the asymptotic biases under contamination of optimal bounded influence estimates and mm estimates are compared

higher order stable generalized finite element method for the elliptic eigenvalue and source problems with an interface in 1d abstract we study the generalized finite element methods gfems for the second order elliptic eigenvalue problem with an interface in 1d the linear stable generalized finite element methods sgfem were recently developed for the elliptic source problem with interfaces we first generalize sgfem to arbitrary order elements and establish the optimal error convergence of the approximate solutions for the elliptic source problem with an interface we then apply the abstract theory of spectral approximation of compact operators to establish the error estimation for the eigenvalue problem with an interface the error estimations on eigenpairs strongly depend on the estimation of the discrete solution operator for the source problem we verify our theoretical findings in various numerical examples including both source and eigenvalue problems

a high order isoparametric finite element method for the computation of waveguide modes we have studied the approximation of optical waveguide eigenvalues by a high order isoparametric vector finite element method isoparametric mappings are used for the approximation of domains with curved boundaries or curved material interfaces eigenvalue convergence for curved elements is investigated numerical results verify the predicted order of convergence and show the remarkable accuracy of the method

binary regression models for contaminated data on etudie la nature des observations aberrantes dans le contexte des donnees de regression binaires on propose un modele simple qui permet qu un petit nombre de reponses binaires soit mal enregistre

eigenvalue approximation by mixed and hybrid methods note univ maryland dept math college pk md 20742 ecole polytech ctr math appl f 91128 palaiseau france univ paris 6 f 75230 paris 05 france mercier b cea limeil f 94190 villeneuve france isi document delivery no lq584times cited 29cited reference count 44 reference asn article 1981 005doi 10 2307 2007651 record created on 2006 08 24 modified on 2017 05 12

outlier tests for logistic regression a conditional approach summary we consider exact conditional methods for identifying outliers in logistic regression data tests for a single outlier and multiple outliers are developed assuming a logistic slippage model the p values for these tests are determined using an explicit enumeration of all possible responses consistent with the observed value of the sufficient statistic justifications are given for preferring this computationally intensive approach to standard methods based on asymptotic approximations the techniques are applied to two examples

nonlinear schrodinger type equations from multiscale reduction of pdes ii necessary conditions of integrability for real pdes the multiscale method has been applied in j math phys 41 6399 2000 to evolution pdes to obtain various nonlinear schrodinger type equations here these results are exploited to derive necessary conditions of integrability for nonlinear real evolution pdes in 1 1 dimensions these conditions are given by explicit formulas and several examples are detailed

analysis of finite element approximation of evolution problems in mixed form this paper deals with the finite element approximation of evolution problems in mixed form following d boffi f brezzi and l gastaldi math comp 69 2000 pp 121 140 we handle separately two types of problems a model for the first case is the heat equation in mixed form while the time dependent stokes problem fits within the second one for either case we give sufficient conditions for a good approximation in the natural functional spaces the results are not obvious in the first situation in this case the well known conditions for the well posedness and convergence of the corresponding steady problem are not sufficient for the good approximation of the time dependent problem this issue is demonstrated with a numerical counter example and justified analytically

short note a primal formulation for the helmholtz decomposition in 1999 jean paul caltagirone and jerome breil have developed in their paper caltagirone j breil sur une methode de projection vectorielle pour la resolution des equations de navier stokes c r acad sci paris 327 serie ii b 1999 1179 1184 a new method to compute a divergence free velocity they have used the grad div operator to extract the solenoidal part of a given vector field in this contribution we explain how this method can be considered as a real helmholtz decomposition and we present a stable approximation in the framework of spectral methods numerical results are presented to illustrate the efficiency of this approach

least median of weighted squares in logistic regression with large strata summary one aim of robust regression is to find estimators with high finite sample breakdown points although various robust estimators have been proposed in logistic regression models their breakdown points are not yet known here it is shown for logistic regression models with binary data that there is no estimator with a high finite sample breakdown point provided the estimator has to fulfill a weak condition in logistic regression models with large strata however a modification of rousseeuw s least median of squares estimator is shown to have a finite sample breakdown point of approximately 2

approximation of eigenvalues in mixed form discrete compactness property and application to hp mixed finite elements abstract in this paper we discuss the discrete compactness property dcp which is a well known tool for the analysis of finite element approximations of maxwell s eigenvalues we restrict our presentation to maxwell s eigenvalues but the theory applies to more general situations and in particular to mixed finite element schemes that can be written in the framework of de rham complex and which enjoy suitable compactness properties we investigate the relationships between dcp and standard mixed conditions for the good approximation of eigenvalues as a consequence of our theory the convergence analysis of the rectangular hp version of raviart thomas finite elements for the approximation of laplace eigenvalues is presented as a corollary of the analogous result for hp edge elements applied to the approximation of maxwell s eigenvalues d boffi m costabel m dauge l demkowicz discrete compactness for the hp version of rectangular edge finite elements siam j numer anal 44 3 2006 979 1004

multiscale reduction of discrete korteweg de vries equations we show how through a multiscale reduction technique performing the analysis at orders beyond the nonlinear schrodinger equation one can effectively prove if some nonlinear partial difference equation is not integrable the example is carried out on a symmetric discretization of the kdv equation and is compared to a similar reduction performed on the integrable lattice potential kdv equation

guaranteed and robust a posteriori bounds for laplace eigenvalues and eigenvectors a unified framework this paper develops a general framework for a posteriori error estimates in numerical approximations of the laplace eigenvalue problem applicable to all standard numerical methods guaranteed and computable upper and lower bounds on an arbitrary simple eigenvalue are given as well as on the energy error in the approximation of the associated eigenvector the bounds are valid under the sole condition that the approximate i th eigenvalue lies between the exact i 1 th and i 1 th eigenvalue where the relative gaps are sufficiently large we give a practical way how to check this the precision of the resulting estimates depends on these relative gaps our bounds feature no unknown solution regularity or polynomial degree dependent constant are optimally convergent efficient and polynomial degree robust under a further explicit a posteriori minimal resolution condition the multiplicative constant in our estimates can be reduced by a fixed factor moreover when an elliptic regularity assumption on the corresponding source problem is satisfied with known constants this multiplicative constant can be brought to the optimal value of 1 with mesh refinement applications of our framework to nonconforming discontinuous galerkin and mixed finite element approximations of arbitrary polynomial degree are provided along with numerical illustrations our key ingredient are equivalences between the i th eigenvalue error the associated eigenvector energy error and the dual norm of the residual we extend them in an appendix to the generic class of bounded below self adjoint operators with compact resolvent

rational eigenvalue problems and applications to photonic crystals we establish new analytic results for a general class of rational spectral problems they arise e g in modelling photonic crystals whose capability to control the flow of light depends on specific

spectral approximation of variationally posed eigenvalue problems by nonconforming methods this paper deals with the nonconforming spectral approximation of variationally posed eigenvalue problems it is an extension to more general situations of known previous results about nonconforming methods as an application of the present theory convergence and optimal order error estimates are proved for the lowest order crouzeix raviart approximation of the eigenpairs of two representative second order elliptical operators

linearization techniques for band structure calculations in absorbing photonic crystals band structure calculations for photonic crystals require the numerical solution of eigenvalue problems in this paper we consider crystals composed of lossy materials with frequency dependent per

spectral approximations by the hdg method we consider the numerical approximation of the spectrum of a secondorder elliptic eigenvalue problem by the hybridizable discontinuous galerkin hdg method we show for problems with smooth eigenfunctions that the approximate eigenvalues and eigenfunctions converge at the rate 2k 1 and k 1 respectively here k is the degree of the polynomials used to approximate the solution its flux and the numerical traces our numerical studies show that a rayleigh quotient like formula applied to certain locally postprocessed approximations can yield eigenvalues that converge faster at the rate 2k 2 for the hdg method as well as for the brezzidouglas marini bdm method we also derive and study a condensed nonlinear eigenproblem for the numerical traces obtained by eliminating all the other variables

discontinuous galerkin computation of the maxwell eigenvalues on simplicial meshes this paper is concerned with the discontinuous galerkin approximation of the maxwell eigenproblem after reviewing the theory developed in a buffa i perugia discontinuous galerkin approximation of the maxwell eigenproblem technical report 24 pv imati cnr pavia italy 2005 we present a set of numerical experiments which both validate the theory and provide further insight regarding the practical performance of discontinuous galerkin methods particularly in the case when non conforming meshes characterized by the presence of hanging nodes are employed

a discrete linearizability test based on multiscale analysis in this paper we consider the classification of dispersive linearizable partial difference equations defined on a quad graph by the multiple scale reduction around their harmonic solution we show that the a1 a2 and a3 linearizability conditions restrain the number of the parameters which enter into the equation a subclass of the equations which pass the a3 c integrability conditions can be linearized by a mobius transformation

the structures and interactions of solitary waves in a 2 1 dimensional coupled nonlinear extension of the reaction diffusion equation the complete integrability of a 2 1 dimensional coupled nonlinear extension of the reaction diffusion cnlerd equation using the technique of painlev p analysis is investigated using the formalism of weiss et al 1983 j math phys 24 522 the arbitrariness of the expansion coefficients are proved besides following the hirota s formalism hirota r 1980 direct methods in soliton theory soliton berlin springer combined to weiss et al s methodology weiss et al 1984 j math phys 25 13 the consistency of the truncation is shown thus without the use of kruskal s simplification the bcklund transformation bt of the equations is obtained via the truncation procedure taking into account the arbitrariness of the expansion coefficients in the foregoing truncation a typical spectrum of localized coherent structures may be unearthed the scattering behavior of such structures is also investigated

on approximation of the eigenvalues of perturbed periodic schrodinger operators this paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic schrodinger operator perturbed by a fast decreasing potential we use a recently developed technique the so called quadratic projection method in order to achieve convergence free from spectral pollution we describe the theoretical foundations of the method in detail and illustrate its effectiveness by several examples

on the linearization of regge calculus we study the linearization of three dimensional regge calculus around euclidean metric we provide an explicit formula for the corresponding quadratic form and relate it to the curl t curl operator which appears in the quadratic part of the einstein hilbert action and also in the linear elasticity complex we insert regge metrics in a discrete version of this complex equipped with densely defined and commuting interpolators we show that the eigenpairs of the curl t curl operator approximated using the quadratic part of the regge action on regge metrics converge to their continuous counterparts interpreting the computation as a non conforming finite element method

a schwarz generalized eigen oscillation spectral element method gesem for 2 d high frequency electromagnetic scattering in dispersive inhomogeneous media in this paper we propose a parallel schwarz generalized eigen oscillation spectral element method gesem for 2 d complex helmholtz equations in high frequency wave scattering in dispersive inhomogeneous media this method is based on the spectral expansion of complex generalized eigen oscillations for the electromagnetic fields and the schwarz non overlapping domain decomposition iteration method the gesem takes advantages of a special real orthogonality property of the complex eigen oscillations and a new radiation interface condition for the system of equations for the spectral expansion coefficients numerical results validate the high resolution and the flexibility of the method for various materials

finite element spectral analysis for the mixed formulation of the elasticity equations the aim of this paper is to analyze the linear elasticity eigenvalue problem formulated in terms of the stress tensor and the rotation this is achieved by considering a mixed variational formulation in which the symmetry of the stress tensor is imposed weakly we show that a discretization of the mixed eigenvalue elasticity problem with reduced symmetry based on the lowest order arnold falk winther element provides a correct approximation of the spectrum we also prove quasi optimal error estimates finally we report some numerical experiments

non conforming high order approximations of the elastodynamics equation in this paper we formulate and analyze two non conforming high order strategies for the approximation of elastic wave problems in heterogeneous media namely the mortar spectral element method and the discontinuous galerkin spectral element method starting from a common variational formulation we make a full comparison of the two techniques from the points of view of accuracy convergence grid dispersion and stability

discontinuous galerkin approximation of the laplace eigenproblem in this paper we analyse the problem of computing eigenvalues and eigenfunctions of the laplace operator by means of discontinuous galerkin dg methods it results that several dg methods actually provide a spectrally correct approximation of the laplace operator we present here the convergence theory which applies to a wide class of dg methods as well as numerical tests demonstrating the theoretical results

extended multilinear variable separation approach and multivalued localized excitations for some 2 1 dimensional integrable systems the multilinear variable separation approach and the related universal formula have been applied to many 2 1 dimensional nonlinear systems starting from the universal formula abundant 2 1 dimensional localized excitations have been found in this paper the universal formula is extended in two different ways one is obtained for the modified nizhnik novikov veselov equation such that two universal terms can be combined linearly and this type of extension is also valid for the 2 1 dimensional symmetric sine gordon system the other is for the dispersive long wave equation the broer kaup kupershmidt system the higher order broer kaup kupershmidt system and the burgers system where arbitrary number of variable separated functions can be involved because of the existence of the arbitrary functions in both the original universal formula and its extended forms the multivalued functions can be used to construct a new type of localized excitations folded solitary waves fsws and foldons the fsws

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

nonlinear schrodinger type equations from multiscale reduction of pdes i systematic derivation in this article we begin a systematic investigation via multiscale expansions of nonlinear evolution pdes partial differential equations in this first article we restrict consideration to a single autonomous but otherwise generic pde in 1 1 variables space time of first order in time whose linear part is dispersive and to solutions dominated by a single plane wave satisfying the linear part of the pde the expansion parameter is an assumedly small coefficient multiplying this plane wave the main indeed asymptotically exact effect of the weak nonlinearity is then to cause a modulation of the amplitude of the plane wave and of its harmonics which is generally described in appropriately defined coarse grained time and space variables by evolution equations of nonlinear schrodinger type a systematic analysis of such equations is presented corresponding to various assumptions on the resonances occurring for the first few harmonics

superconvergence of the local discontinuous galerkin method for elliptic problems on cartesian grids in this paper we present a superconvergence result for the local discontinuous galerkin ldg method for a model elliptic problem on cartesian grids we identify a special numerical flux for which the l2 norm of the gradient and the l2 norm of the potential are of orders k 1 2 and k 1 respectively when tensor product polynomials of degree at most k are used for arbitrary meshes this special ldg method gives only the orders of convergence of k and k 1 2 respectively we present a series of numerical examples which establish the sharpness of our theoretical results

two families of mixed finite elements for second order elliptic problems two families of mixed finite elements one based on triangles and the other on rectangles are introduced as alternatives to the usual raviart thomas nedelec spaces error estimates inl 2 andh 5 are derived for these elements a hybrid version of the mixed method is also considered and some superconvergence phenomena are discussed

a stabilized finite element method for the two field and three field stokes eigenvalue problems in this paper the stabilized finite element approximation of the stokes eigenvalue problems is considered for both the two field displacement pressure and the three field stress displacement pressure formulations the method presented is based on a subgrid scale concept and depends on the approximation of the unresolvable scales of the continuous solution in general subgrid scale techniques consist in the addition of a residual based term to the basic galerkin formulation the application of a standard residual based stabilization method to a linear eigenvalue problem leads to a quadratic eigenvalue problem in discrete form which is physically inconvenient as a distinguished feature of the present study we take the space of the unresolved subscales orthogonal to the finite element space which promises a remedy to the above mentioned complication in essence we put forward that only if the orthogonal projection is used the residual is simplified and the use of term by term stabilization is allowed thus we do not need to put the whole residual in the formulation and the linear eigenproblem form is recovered properly we prove that the method applied is convergent and present the error estimates for the eigenvalues and the eigenfunctions we report several numerical tests in order to illustrate that the theoretical results are validated

on mass conservation in least squares methods we compare three least squares finite element reformulations of the stokes equations paying particular attention to mass conservation the first problem we approximate has a simple analytical solution over a convex region even for this simple problem without special treatment of the conservation of mass term very poor numerical solutions may result sufficiently weighting this term leads to a dramatic improvement in the results over a range of test problems

optimally bounded score functions for generalized linear models with applications to logistic regression summary we study optimally bounded score functions for estimating regression parameters in a generalized linear model our work extends results obtained by krasker welsch 1982 for the linear model and provides a simple proof of krasker welsch s first order condition for strong optimality the application of these results to logistic regression is studied in some detail with an example given comparing the bounded influence estimator with maximum likelihood where h q and c are known functions and 0 is a vector of regression parameters models of this type include logistic and probit regression poisson regression linear regression with known variance and certain models for lifetime data our motivation for seeking robust estimators is the same as that in the linear model maximum likelihood estimation is sometimes sensitive to outlying data for logistic regression pregibon 1981 1982 has documented the nonrobustness of the maximum likelihood estimator and expounded the benefits of diagnostics as well as robust or resistant fitting procedures see also johnson 1985 much of the work on robust estimation concerns finding estimators which sacrifice little efficiency at the assumed model while providing protection against outliers and model violations we follow this course finding bounded influence estimators minimizing certain functionals of the asymptotic covariance matrix related work includes that of hampel 1978 krasker 1980 and krasker welsch 1982 when fitting models to data two important issues are identification of outliers and influential cases and accommodation of these observations frequently when influential cases are present the fitted model is not representative of the bulk of the data to rectify this one can simply delete influential cases and refit via standard methods but this

on the problem of spurious eigenvalues in the approximation of linear elliptic problems in mixed form in the approximation of linear elliptic operators in mixed form it is well known that the so called inf sup and ellipticity in the kernel properties are sufficient and in a sense to be made precise necessary in order to have good approximation properties and optimal error bounds one might think in the spirit of mercier osborn rappaz raviart and in consideration of the good behavior of commonly used mixed elements like raviart thomas or brezzi douglas marini elements that these conditions are also sufficient to ensure good convergence properties for eigenvalues in this paper we show that this is not the case in particular we present examples of mixed finite element approximations that satisfy the above properties but exhibit spurious eigenvalues such bad behavior is proved analytically and demonstrated in numerical experiments we also present additional assumptions fulfilled by the commonly used mixed methods already mentioned which guarantee optimal error bounds for eigenvalue approximations as well

mixed discontinuous galerkin approximation of the elasticity eigenproblem we introduce a discontinuous galerkin method for the mixed formulation of the elasticity eigenproblem with reduced symmetry the analysis of the resulting discrete eigenproblem does not fit in the standard spectral approximation framework since the underlying source operator is not compact and the scheme is nonconforming we show that the proposed scheme provides a correct approximation of the spectrum and prove asymptotic error estimates for the eigenvalues and the eigenfunctions finally we provide several numerical tests to illustrate the performance of the method and confirm the theoretical results

discontinuous galerkin methods of the non selfadjoint steklov eigenvalue problem in inverse scattering abstract in this paper we apply discontinuous galerkin methods to the non selfadjoint steklov eigenvalue problem arising in inverse scattering the variational formulation of the problem is non selfadjoint and does not satisfy h1 elliptic condition by using the spectral approximation theory of compact operators we prove the spectral approximation and optimal convergence order for the eigenvalues finally some numerical experiments are reported to show that the proposed numerical schemes are efficient for real and complex steklov eigenvalues

new integrable pdes of boomeronic type novel integrable systems of coupled first order autonomous pdes in 1 1 dimensions space x and time t are presented integrable covariant 2 vector and 3 vector pdes as well as higher order integrable pdes for a single or a couple of scalar dependent variables including an extension of the sine gordon equation and a remarkably neat highly nonlinear third order pde are also obtained by appropriate reductions of the basic matrix equations the lax pairs that characterize the integrable character of the basic matrix pdes are also exhibited as well as their single soliton solutions these solitons generally exhibit the boomeronic and less generically the trapponic phenomenology namely they do not move uniformly but rather in an appropriate reference system come in from one end in the remote past and boomerang back to that same end in the remote future boomerons or are trapped to oscillate around a value fixed by the initial data trappons

mixed finite element methods in fluid structure systems the eigenvalue problem describing the frequencies of a fluid vibrating in a rigid cavity or within moving boundaries is considered based on the method of lagrange multipliers a three field mixed formulation is introduced in order to avoid the spurious circulating modes stability and optimal error bounds are proved for two choices of finite element spaces

an a posteriori estimator of eigenvalue eigenvector error for penalty type discontinuous galerkin methods we provide an abstract framework for analyzing discretization error for eigenvalue problems discretized by discontinuous galerkin methods such as the local discontinuous galerkin method and symmetric interior penalty discontinuous galerkin method the analysis applies to clusters of eigenvalues that may include degenerate eigenvalues we use asymptotic perturbation theory for linear operators to analyze the dependence of eigenvalues and eigenspaces on the penalty parameter we first formulate the dg method in the framework of quadratic forms and construct a companion infinite dimensional eigenvalue problem with the use of the companion problem the eigenvalue vector error is estimated as a sum of two components the first component can be viewed as a non conformity error that we argue can be neglected in practical estimates by properly choosing the penalty parameter the second component is estimated a posteriori using auxiliary subspace techniques and this constitutes the practical estimate

stable and semistable low order finite elements for viscous flows it is shown that i the bilinear constant and linear constant box elements are not uniformly stable and ii certain element pairs derived from those above by restricting the pressure spaces are stable the notion of div semistability is developed to study the behavior of the bilinear constant and linear constant box elements in detail

mathematical analysis of a finite element method without spurious solutions for computation of dielectric waveguides in this paper we propose a finite element method to compute dielectric waveguides which does not present spurious solutions in addition to a theoretical analysis showing the good stability properties of this method we give numerical results for some classical test problems

immersed finite element method for eigenvalue problem abstract we consider the approximation of elliptic eigenvalue problem with an interface the main aim of this paper is to prove the stability and convergence of an immersed finite element method ifem for eigenvalues using crouzeix raviart p 1 nonconforming approximation we show that spectral analysis for the classical eigenvalue problem can be easily applied to our model problem we analyze the ifem for elliptic eigenvalue problems with an interface and derive the optimal convergence of eigenvalues numerical experiments demonstrate our theoretical results

the asymptotics of s estimators in the linear regression model we consider the consistency and weak convergence of s estimators in the linear regression model sufficient conditions for consistency with varying dimension are given which are sufficiently weak to cover for example polynomial trends and i i d carriers a weak convergence theorem for the hampel rousseeuw least median of squares estimator is obtained and it is shown under rather general conditions that the correct norming factor is n 1 3 finally the asymptotic normality of s estimators with a smooth rho function is obtained again under weak conditions on the carriers

least median of squares regression abstract classical least squares regression consists of minimizing the sum of the squared residuals many authors have produced more robust versions of this estimator by replacing the square by something else such as the absolute value in this article a different approach is introduced in which the sum is replaced by the median of the squared residuals the resulting estimator can resist the effect of nearly 50 of contamination in the data in the special case of simple regression it corresponds to finding the narrowest strip covering half of the observations generalizations are possible to multivariate location orthogonal regression and hypothesis testing in linear models

on robustness properties of convex risk minimization methods for pattern recognition the paper brings together methods from two disciplines machine learning theory and robust statistics we argue that robustness is an important aspect and we show that many existing machine learning methods based on the convex risk minimization principle have besides other good properties also the advantage of being robust robustness properties of machine learning methods based on convex risk minimization are investigated for the problem of pattern recognition assumptions are given for the existence of the influence function of the classifiers and for bounds on the influence function kernel logistic regression support vector machines least squares and the adaboost loss function are treated as special cases some results on the robustness of such methods are also obtained for the sensitivity curve and the maxbias which are two other robustness criteria a sensitivity analysis of the support vector machine is given

projection estimators for generalized linear models we introduce a new class of robust estimators for generalized linear models which is an extension of the class of projection estimators for linear regression these projection estimators are defined using an initial robust estimator for a generalized linear model with only one unknown parameter we found a bound for the maximum asymptotic bias of the projection estimator caused by a fraction e of outlier contamination for small e this bias is approximately twice the maximum bias of the initial estimator independently of the number of regressors since these projection estimators are not asymptotically normal we define one step weighted m estimators starting at the projection estimators these estimators have the same asymptotic normal distribution as the m estimator and a degree of robustness close to the one of the projection estimator we perform a monte carlo simulation for the case of binomial and poisson regression with canonical links this study shows that the proposed estimators compare favorab

conditionally unbiased bounded influence estimation in general regression models with applications to generalized linear models abstract in this article robust estimation in generalized linear models for the dependence of a response y on an explanatory variable x is studied a subclass of the class of m estimators is defined by imposing the restriction that the score function must be conditionally unbiased given x within this class of conditionally fisher consistent estimators optimal bounded influence estimators of regression parameters are identified and their asymptotic properties are studied the estimators studied in this article and the efficient bounded influence estimators studied by stefanski carroll and ruppert 1986 depend on an auxiliary centering constant and nuisance matrix the centering constant can be given explicitly for the conditionally fisher consistent estimators and thus they are easier to compute than the estimators studied by stefanski et al 1986 in addition estimation of the nuisance matrix has no effect on the asymptotic distribution of the conditionally fisher consistent estimators the sam

localized excitations in 2 1 dimensional systems by means of a special variable separation approach a common formula with some arbitrary functions has been obtained for some suitable physical quantities of various 2 1 dimensional models such as the davey stewartson ds model the nizhnik novikov veselov nnv system asymmetric nnv equation asymmetric ds equation dispersive long wave equation broer kaup kupershmidt system long wave short wave interaction model maccari system and a general n m component ablowitz kaup newell segur akns system selecting the arbitrary functions appropriately one may obtain abundant stable localized interesting excitations such as the multidromions lumps ring soliton solutions breathers instantons etc it is shown that some types of lower dimensional chaotic patterns such as the chaotic chaotic patterns periodic chaotic patterns chaotic line soliton patterns chaotic dromion patterns fractal lump patterns and fractal dromion patterns may be found in higher dimensional soliton systems the interactions between the traveling ring type soliton solutions are completely elastic the traveling ring solitons pass through each other and preserve their shapes velocities and phases some types of localized weak solutions peakons are also discussed especially the interactions between two peakons are not completely elastic after the interactions the traveling peakons also pass through each other and preserve their velocities and phases however they completely exchange their shapes

consistency and asymptotic normality of the maximum likelihood estimator in generalized linear models generalized linear models are used for regression analysis in a number of cases including categorical responses where the classical assumptions are violated the statistical analysis of such models is based on the asymptotic properties of the maximum likelihood estimator we present mild general conditions which respectively assure weak or strong consistency or asymptotic normality most of the previous work has been concerned with natural link functions in this case our normality condition though obtained by a different approach is closely related to a condition of haberman 1977a examples show how the general conditions reduce to weak requirements for special exponential families further for regressors with a compact range sufficient conditions are given which do not involve the unknown parameter and are therefore easy to check in practice responses with a bounded range e g categorical responses and stochastic regressors also are treated

the multiscale expansions of difference equations in the small lattice spacing regime and a vicinity and integrability test i we propose an algorithmic procedure i to study the distance between an integrable pde and any discretization of it in the small lattice spacing regime and at the same time ii to test the asymptotic integrability properties of such discretization this method should provide in particular useful and concrete information on how good is any numerical scheme used to integrate a given integrable pde the procedure illustrated on a fairly general ten parameter family of discretizations of the nonlinear schr dinger equation consists of the following three steps i the construction of the continuous multiscale expansion of a generic solution of the discrete system at all orders in following degasperis et al 1997 physica d 100 187 211 ii the application to such an expansion of the degasperis procesi dp integrability test degasperis a and procesi m 1999 asymptotic integrability symmetry and perturbation theory spt98 ed a degasperis and g gaeta singapore world scientific pp 23 37 degasperis a 2001 multiscale expansion and integrability of dispersive wave equations lectures given at the euro summer school what is integrability isaac newton institute cambridge uk 13 24 august integrability lecture notes in physics vol 767 ed a mikhailov berlin springer to test the asymptotic integrability properties of the discrete system and its distance from its continuous limit iii the use of the main output of the dp test to construct infinitely many approximate symmetries and constants of motion of the discrete system through novel and simple formulas

least absolute deviations fits for generalized linear models reference stap article 1992 004view record in web of science record created on 2006 04 04 modified on 2016 08 08

discrete third order spectral problems and a new toda type equation in this paper we construct the class of equations associated with a discrete spectral problem of third order among the equations of this class we find an integrable differential equation on the lattice with exponential nonlinearity by considering its associated darboux transformation we construct an explicit solution

multiple scale perturbation beyond the nonlinear schroedinger equation i abstract we consider the effect of weak nonlinearity on the propagation of one dimensional strongly dispersive waves in the standard quasi monochromatic approximation it is well known that the first order amplitude modulation satisfies the nonlinear schroedinger equation in slow variables with the assumption that this amplitude modulation has no discrete spectrum component i e no soliton we explore the higher order effects and provide a well defined procedure to compute all coefficients of the perturbative expansion as relatively bounded functions no secularity effects of slow variables the main effect of this procedure is that the leading amplitude modulation satisfies at higher orders the nonlinear schroedinger hierarchy of evolution equations in slow variables key ingredient is the integrability of the nonlinear schroedinger equation and its commuting symmetries

threshold dose response models in toxicology summary after a brief discussion of the threshold concept in toxicology we consider models for the estimation of thresholds in the case where the observed response is binary or quantal a generalization of the four parameter tukey lambda family of distributions is proposed as a useful class of models for threshold estimation properties of these models are discussed and the process of model fitting and evaluation is illustrated using a number of data sets the discussion includes consideration of background or spontaneous response and comparison with other models one of these is the linearplateau or hockey stick model which has been used in a number of toxicological studies

on the convergence of second order spectra and multiplicity the notion of second order relative spectrum of a self adjoint operator acting on a hilbert space has been studied recently in connection with the phenomenon of spectral pollution in the galerkin method in this paper we examine how the second order spectrum encodes precise information about the multiplicity of the isolated eigenvalues of the underlying operator our theoretical findings are supported by various numerical experiments on the computation of guaranteed eigenvalue inclusions via finite element bases

on least squares finite element methods for the poisson equation and their connection to the dirichlet and kelvin principles least squares finite element methods for first order formulations of the poisson equation are not subject to the inf sup condition and lead to stable solutions even when all variables are approximated by equal order continuous finite element spaces for such elements one can also prove optimal convergence in the energy norm equivalent to a norm on h 1 omega times h omega mbox rm div for all variables and optimal l2 convergence for the scalar variable however showing optimal l2 convergence for the flux has proven to be impossible without adding the redundant curl equation to the first order system of partial differential equations in fact numerical evidence strongly suggests that nodal continuous flux approximations do not posses optimal l2 accuracy in this paper we show that optimal l2 error rates for the flux can be achieved without the curl constraint provided that one uses the div conforming family of brezzi douglas marini or brezzi douglas duran fortin elements then we proceed to reveal an interesting connection between a least squares finite element method involving h omega mbox rm div conforming flux approximations and mixed finite element methods based on the classical dirichlet and kelvin principles we show that such least squares finite element methods can be obtained by approximating through an l2 projection the hodge operator that connects the kelvin and dirichlet principles our principal conclusion is that when implemented in this way a least squares finite element method combines the best computational properties of finite element methods based on each of the classical principles

on the penalty stabilization mechanism for upwind discontinuous galerkin formulations of first order hyperbolic systems abstract penalty fluxes are dissipative numerical fluxes for high order discontinuous galerkin dg methods which depend on a penalization parameter warburton 2013 ye et al 2016 we investigate the dependence of the spectra of high order dg discretizations on this parameter and show that as its value increases the spectrum of the dg discretization splits into two disjoint sets of eigenvalues one set converges to the eigenvalues of a conforming discretization while the other set corresponds to spurious eigenvalues which are damped proportionally to numerical experiments also demonstrate that undamped spurious modes present in both in the limit of zero and large penalization parameters are damped for moderate values of the upwind parameter

resistant fits for some commonly used logistic models with medical application logistic regression type models are used in many applications some examples include the classical dose response experiment prospective and retrospective studies of disease incidence with and without matching and the analysis of ordinal data in most instances the model is fitted by the method of maximum likelihood which like least squares is sensitive to atypical observations an alternative to maximum likelihood is proposed and illustrated by examples

the p and hp versions of the virtual element method for elliptic eigenvalue problems abstract we discuss the p and h p versions of the virtual element method for the approximation of eigenpairs of elliptic operators with a potential term on polygonal meshes an application of this model is provided by the schrodinger equation with a pseudo potential term as an interesting byproduct we present for the first time in literature an explicit construction of the stabilization of the mass matrix we present in detail the analysis of the p version of the method proving exponential convergence in the case of analytic eigenfunctions the theoretical results are supplied with a wide set of experiments we also show numerically that in the case of eigenfunctions with finite sobolev regularity an exponential approximation of the eigenvalues in terms of the cubic root of the number of degrees of freedom can be obtained by employing h p refinements importantly the geometric flexibility of polygonal meshes is exploited in the construction of the h p spaces

universal c integrable nonlinear partial differential equation in n 1 dimensions a nonlinear partial differential equation of evolution in n 1 dimensions is exhibited which is c integrable namely integrable via an appropriate change of variables and which also possesses an element of universality as it is obtained by applying a limiting procedure to a class of nonlinear partial differential equations since this limiting procedure corresponds to physical conditions likely to prevail in some phenomenological circumstances it is expected that this equation shall have applicative relevance but this possibility is not pursued in this paper the method whereby this equation has been obtained as well as its integrable character qualify it as a n 1 dimensional analog of the eckhaus equation to which it does indeed reduce for n 1

on the spurious solutions in the high order finite difference methods for eigenvalue problems in this paper the origins of spurious solutions occurring in the high order finite difference methods are studied based on a uniform mesh spurious modes are found in the high order one sided finite difference discretizations of many eigenvalue problems spurious modes are classified as spectral pollution and non spectral pollution the latter can be partially avoided by mesh refinement while the former persists when the mesh is refined through numerical studies of some prototype eigenvalue problems such as those of the helmholtz and beam equations we show that perfect central differentiation schemes do not produce any spurious modes nevertheless high order central difference schemes encounter difficulties in implementing complex boundary conditions we further show that the central difference schemes will produce spurious modes as well if asymmetric approximation is involved in boundary treatments in general central difference schemes are less likely to produce spurious modes than one sided difference schemes 2007 elsevier b v all rights reserved

analysis of some mixed finite element methods related to reduced integration we prove error estimates for the following two mixed finite element methods related to reduced integration a method for stokes problem using rectangular elements with piecewise bilinear approximations for the velocities and piecewise constants for the pressure and one method for a plate problem using bilinear approximations for transversal displacement and rotations and piecewise constants for the shear stress the main idea of the proof in the case of stokes problem is to combine a weak babuska brezzi type stability estimate for the pressure with a superapproximability property for the velocities a similar technique is used in the case of the plate problem