spline smoothing over difficult regions summary it is occasionally necessary to smooth data over domains in ir2 with complex irregular boundaries or interior holes traditional methods of smoothing which rely on the euclidean metric or which measure smoothness over the entire real plane may then be inappropriate this paper introduces a bivariate spline smoothing function defined as the minimizer of a penalized sum of squares functional the roughness penalty is based on a partial differential operator and is integrated only over the problem domain by using finite element analysis the method is motivated by and applied to two sample smoothing problems and is compared with the thin plate spline

nonlinear aggregation diffusion equations radial symmetry and long time asymptotics we analyze under which conditions equilibration between two competing effects repulsion modeled by nonlinear diffusion and attraction modeled by nonlocal interaction occurs this balance leads to continuous compactly supported radially decreasing equilibrium configurations for all masses all stationary states with suitable regularity are shown to be radially symmetric by means of continuous steiner symmetrization techniques calculus of variations tools allow us to show the existence of global minimizers among these equilibria finally in the particular case of newtonian interaction in two dimensions they lead to uniqueness of equilibria for any given mass up to translation and to the convergence of solutions of the associated nonlinear aggregation diffusion equations towards this unique equilibrium profile up to translations as t rightarrow infty

the ii p method for estimating multivariate functions from noisy data the method for estimating an underlying smooth function of m variables x l xm using noisy data is based on approximating it by a sum of products of the form m m x m the problem is then reduced to estimating the univariate functions in the products a convergent algorithm is described the method keeps tight control on the degrees of freedom used in the fit many examples are given the quality of fit given by the method is excellent usually only a few products are enough to fit even fairly complicated functions the coding into products of univariate functions allows a relatively understandable interpretation of the multivariate fit

large systems of interacting particles and the porous medium equation abstract we study the empirical processes of systems of interacting particles whose time evolution is given by coupled ordinary differential equations in particular as the population size tends to infinity we derive different versions of the porous medium equation as limit dynamics

nonparametric quasi maximum likelihood estimation for gaussian locally stationary processes this paper deals with nonparametric maximum likelihood estimation for gaussian locally stationary processes our nonparametric mle is constructed by minimizing a frequency domain likelihood over a class of functions the asymptotic behavior of the resulting estimator is studied the results depend on the richness of the class of functions both sieve estimation and global estimation are considered our results apply in particular to estimation under shape constraints as an example autoregressive model fitting with a monotonic variance function is discussed in detail including algorithmic considerations a key technical tool is the time varying empirical spectral process indexed by functions for this process a bernstein type exponential inequality and a central limit theorem are derived these results for empirical spectral processes are of independent interest

accelerated direct solution of electromagnetic scattering via characteristic basis function method with sherman morrison woodbury formula based algorithm the characteristic basis function method has been proposed to accelerate the direct solution of the method of moments by reducing the number of unknowns however with the increase in the target size the reduced matrix will still become too large to directly solve and store in this communication the algorithm based on the sherman morrison woodbury smw formula is employed to address this problem for the first time it compresses the reduced matrix into a product of block diagonal matrices with the aid of the smw formula and the adaptive cross approximation subsequently the inverse of the reduced matrix can be easily obtained by the inverses of these block diagonal matrices the numerical results about the electromagnetic scattering are shown to demonstrate the performance of the proposed method

equilibria of homogeneous functionals in the fair competition regime we consider macroscopic descriptions of particles where repulsion is modelled by non linear power law diffusion and attraction by a homogeneous singular non singular kernel leading to variants of the keller segel model of chemotaxis we analyse the regime in which both homogeneities scale the same with respect to dilations that we coin as fair competition in the singular kernel case we show that existence of global equilibria can only happen at a certain critical value and they are characterised as optimisers of a variant of hls inequalities we also study the existence of self similar solutions for the sub critical case or equivalently of optimisers of rescaled free energies these optimisers are shown to be compactly supported radially symmetric and non increasing stationary solutions of the non linear keller segel equation on the other hand we show that no radially symmetric non increasing stationary solutions exist in the non singular kernel case implying that there is no criticality however we show the existence of positive self similar solutions for all values of the parameter under the condition that diffusion is not too fast we finally illustrate some of the open problems in the non singular kernel case by numerical experiments

block size optimization of cbfm for scattering problems the characteristic basis function method cbfm was developed as an algorithm to accelerate the analysis based on direct matrix solver in cbfm the optimum block size greatly influences the overall analysis time in this paper we propose a guideline for setting the optimal block size that can be applied to every algorithm based on cbfm rough estimation of the optimal block size is l b rough approx 0 05 n 6 29 and the exact optimal block size can be determined through preprocessing based on rough estimation numerical results of electromagnetic scattering problems are shown to demonstrate the performance of the proposed method

local spectral analysis via a bayesian mixture of smoothing splines in many practical problems time series are realizations of nonstationary random processes these processes can often be modeled as processes with slowly changing dynamics or as piecewise stationary processes in these cases various approaches to estimating the time varying spectral density have been proposed our approach in this article is to estimate the log of the dahlhaus local spectrum using a bayesian mixture of splines the basic idea of our approach is to first partition the data into small sections we then assume that the log spectral density of the evolutionary process in any given partition is a mixture of individual log spectra we use a mixture of smoothing splines model with time varying mixing weights to estimate the evolutionary log spectrum the mixture model is fit using markov chain monte carlo techniques that yield estimates of the log spectra of the individual subsections in addition to an estimate of the local log spectral density the method yields pointwise credible intervals

solution of electrically large problems with multilevel characteristic basis functions we present a multilevel version to the characteristic basis function method cbfm this technique extends the range of applicability of the conventional cbfm and allows a direct solution of problems even when they exceed 250 000 degrees of freedom in this paper it is shown how we can use the multilevel cbfm which is a natural extension of the conventional approach and which saves both time and memory and yet retains excellent accuracy in the computed far fields also the adaptive cross algorithm is used for fast calculation of the interaction between the blocks in the process of generating the reduced matrix

functional inequalities thick tails and asymptotics for the critical mass patlak keller segel model we investigate the long time behavior of the critical mass patlak keller segel equation this equation has a one parameter family of steady state solutions rhohls lambda 0 with thick tails whose second moment is not bounded we show that these steady state solutions are stable and find basins of attraction for them using an entropy functional fcfd coming from the critical fast diffusion equation in r 2 we construct solutions of patlak keller segel equation satisfying an entropy entropy dissipation inequality for fcfd while the entropy dissipation for fcfd is strictly positive it turns out to be a difference of two terms neither of which need to be small when the dissipation is small we introduce a strategy of em controlled concentration to deal with this issue and then use the regularity obtained from the entropy entropy dissipation inequality to prove the existence of basins of attraction for each stationary state composed by certain initial data converging towards rhohls in the present paper we do not provide any estimate of the rate of convergence but we discuss how this would result from a stability result for a certain sharp gagliardo nirenberg sobolev inequality

symmetrization techniques on unbounded domains application to a chemotaxis system on rn the authors study the parabolic elliptic system on rn u t u u v 0 v v u u 0 u0 a version of the mathematical model of chemotaxis proposed by keller and segel a differential inequality for the quantity s0u t d where u is the decreasing rearrangement of the solution u t with respect to the spatial variable is obtained as a consequence they obtain e g lp bounds of the solution u v on r2 and global in time existence of solutions under the condition r2u0 8 then the solution u v blows up in a finite time compared to the previous work of diaz diaz and nagai adv math sci appl 5 1995 no 2 659 680 mr1361010 96j 35246 where this problem has been considered on bounded domains of rn there are some additional technical difficulties connected with the regularity of the derivative u t

updating the inverse of a matrix the sherman morrison woodbury formulas relate the inverse of a matrix after a small rank perturbation to the inverse of the original matrix the history of these fomulas is presented and various applications to statistics networks structural analysis asymptotic analysis optimization and partial differential equations are discussed the sherman morrison woodbury formulas express the inverse of a matrix after a small rank perturbation in terms of the inverse of the original matrix this paper surveys the history of these formulas and we examine some applications where these formulas are helpful

on explosions of solutions to a system of partial differential equations modelling chemotaxis a system of partial differential equations modelling chemotactic aggregation is analysed keller segel model conditions on the system of paramaters are given implying global existence of smooth solutions in two space dimensions and radially symmetric situations explosion of the bacteria concentration in finite time is shown for a class of initial values

testing the parametric null model hypothesis in semiparametric partial and generalized spline models on etend les resultats de cox et koh 1986 aux modeles generalises de wahba 1985 et a divers autres modeles splines partiels on montre que la statistique de test a une relation etroite avec le comportement de la fonction de validation croisee generalisee

flexible parsimonious smoothing and additive modeling a simple method is presented for fitting regression models that are nonlinear in the explanatory variables despite its simplicity or perhaps because of it the method has some powerful characteristics that cause it to be competitive with and often superior to more sophisticated techniques especially for small data sets in the presence of high noise

diagnostics for nonparametric regression models with additive terms abstract recent developments of multivariate smoothing methods provide a rich collection of feasible models for nonparametric multivariate data analysis among the most interpretable are models with additive terms construction of various models and algorithms for computing the models have been the main concern of the existing literature in this area few results are available on the validation of computed fits and many applications of nonparametric methods unfortunately end up interpreting the noise this article proposes and illustrates some simple retrospective diagnostics to help data analysts in detecting possible aliasing effects in computed nonparametric fits and in building parsimonious models in an interactive fashion it also discusses the concepts and rationale behind the proposal including concurvity diagnostics versus tests and so forth for their ready availability interaction splines are used in the illustrations

sparsified adaptive cross approximation algorithm for accelerated method of moments computations this paper presents a modification of the adaptive cross approximation aca algorithm for accelerated solution of the method of moments linear system for electrically large radiation and scattering problems as with aca subblocks of the impedance matrix that represent the interaction between well separated subdomains are substituted by compressed approximations allowing for reduced storage and accelerated iterative solution the modified algorithm approximates the original subblocks with products of sparse matrices constructed with the aid of the aca algorithm and of a sub sampling of the original basis functions belonging to either subdomain because of the sampling an additional error is introduced with respect to aca but this error is controllable just like ordinary aca sparsified aca is kernel independent and needs no problem specific information except for the topology of the basis functions as a numerical example rcs computations of the nasa almond are presented showing an important gain in efficiency furthermore the numerical experiment reveals a computational complexity close to n logn for sparsified aca for a target electrical size of up to 50 wavelengths

hierarchical matrix techniques based on matrix decomposition algorithm for the fast analysis of planar layered structures the matrix decomposition algorithm mda provides an efficient matrix vector product for the iterative solution of the integral equation ie by a blockwise compression of the impedance matrix the mda with a singular value decomposition svd recompression scheme i e so called mda svd method shows strong ability for the analysis of planar layered structures however iterative solution faces the problem of convergence rate an efficient hierarchical h lu decomposition algorithm based on the h matrix techniques is proposed to handle this problem exploiting the data sparse representation of the mda svd compressed impedance matrix h lu decomposition can be efficiently implemented by h matrix arithmetic h matrix techniques provide a flexible way to control the accuracy of the approximate h lu factors h lu decomposition with low accuracy can be used as an efficient preconditioner for the iterative solver due to its low computational cost while h lu decomposition with high accuracy can be used as a direct solver for dealing with multiple right hand side rhs vector problems particularly numerical examples demonstrate that the proposed method is very robust for the analysis of various planar layered structures

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

bayesian confidence intervals for the cross validated smoothing spline summary we consider the model y t g ti ei i 17 2 n where g t t 0 1 is a smooth function and the ei are independent n 0 a2 errors with g2 unknown the cross validated smoothing spline can be used to estimate g non parametrically from

congested aggregation via newtonian interaction we consider a congested aggregation model that describes the evolution of a density through the competing effects of nonlocal newtonian attraction and a hard height constraint this provides a counterpoint to existing literature on repulsive attractive nonlocal interaction models where the repulsive effects instead arise from an interaction kernel or the addition of diffusion we formulate our model as the wasserstein gradient flow of an interaction energy with a penalization to enforce the constraint on the height of the density from this perspective the problem can be seen as a singular limit of the keller segel equation with degenerate diffusion two key properties distinguish our problem from previous work on height constrained equations nonconvexity of the interaction kernel which places the model outside the scope of classical gradient flow theory and nonlocal dependence of the velocity field on the density which causes the problem to lack a comparison principle to overcome these obstacles we combine recent results on gradient flows of nonconvex energies with viscosity solution theory we characterize the dynamics of patch solutions in terms of a hele shaw type free boundary problem and using this characterization show that in two dimensions patch solutions converge to a characteristic function of a disk in the long time limit with an explicit rate on the decay of the energy we believe that a key contribution of the present work is our blended approach combining energy methods with viscosity solution theory

approximation of boundary element matrices this article considers the problem of approximating a general asymptotically smooth function in two variables typically arising in integral formulations of boundary value problems by a sum of products of two functions in one variable from these results an iterative algorithm for the low rank approximation of blocks of large unstructured matrices generated by asymptotically smooth functions is developed this algorithm uses only few entries from the original block and since it has a natural stopping criterion the approximative rank is not needed in advance

automatic statistical analysis of bivariate nonstationary time series we propose a new method for analyzing bivariate nonstationary time series the proposed method is a statistical procedure that automatically segments the time series into approximately stationary blocks and selects the span to be used to obtain the smoothed estimates of the time varying spectra and coherence it is based on the smooth localized complex exponential slex transform which forms a library of orthogonal complex valued transforms that are simultaneously localized in time and frequency we show that the smoothed slex periodograms are consistent estimators report simulation results and apply the method to a two channel electroencephalogram dataset recorded during an epileptic seizure

some tools for functional data analysis multivariate data analysis permits the study of observations which are finite sets of numbers but modern data collection situations can involve data or the processes giving rise to them which are functions functional data analysis involves infinite dimensional processes and or data the paper shows how the theory of l splines can support generalizations of linear modelling and principal components analysis to samples drawn from random functions spline smoothing rests on a partition of a function space into two orthogonal subspaces one of which contains the obvious or structural components of variation among a set of observed functions and the other of which contains residual components this partitioning is achieved through the use of a linear differential operator and we show how the theory of polynomial splines can be applied more generally with an arbitrary operator and associated boundary constraints these data analysis tools are illustrated by a study of variation in temperature precipitation patterns among some canadian weather stations

conditional adaptive bayesian spectral analysis of nonstationary biomedical time series summary many studies of biomedical time series signals aim to measure the association between frequency domain properties of time series and clinical and behavioral covariates however the time varying dynamics of these associations are largely ignored due to a lack of methods that can assess the changing nature of the relationship through time this article introduces a method for the simultaneous and automatic analysis of the association between the time varying power spectrum and covariates which we refer to as conditional adaptive bayesian spectrum analysis cabs the procedure adaptively partitions the grid of time and covariate values into an unknown number of approximately stationary blocks and nonparametrically estimates local spectra within blocks through penalized splines cabs is formulated in a fully bayesian framework in which the number and locations of partition points are random and fit using reversible jump markov chain monte carlo techniques estimation and inference averaged over the distribution of partitions allows for the accurate analysis of spectra with both smooth and abrupt changes the proposed methodology is used to analyze the association between the time varying spectrum of heart rate variability and self reported sleep quality in a study of older adults serving as the primary caregiver for their ill spouse

wavelet thresholding in anisotropic function classes and application to adaptive estimation of evolutionary spectra we derive minimax rates for estimation in anisotropic smoothness classes this rate is attained by a coordinatewise thresholded wavelet estimator based on a tensor product basis with separate scale parameter for every dimension it is shown that this basis is superior to its one scale multiresolution analog if different degrees of smoothness in different directions are present as an important application we introduce a new adaptive wavelet estimator of the time dependent spectrum of a locally stationary time series using this model which was resently developed by dahlhaus we show that the resulting estimator attains nearly the rate which is optimal in gaussian white noise simultaneously over a wide range of smoothness classes moreover by our new approach we overcome the difficulty of how to choose the right amount of smoothing i e how to adapt to the appropriate resolution for reconstructing the local structure of the evolutionary spectrum in the time frequency plane

fast analysis of large antenna arrays using the characteristic basis function method and the adaptive cross approximation algorithm the characteristic basis function method cbfm has been hybridized with the adaptive cross approximation aca algorithm to construct a reduced matrix equation in a time efficient manner and to solve electrically large antenna array problems in core with a solve time orders of magnitude less than those in the conventional methods various numerical examples are presented that demonstrate that the proposed method has a very good accuracy computational efficiency and reduced memory storage requirement specifically we analyze large 1 d and 2 d arrays of electrically interconnected tapered slot antennas tsas the entire computational domain is subdivided into many smaller subdomains each of which supports a set of characteristic basis functions cbfs we also present a novel scheme for generating the cbfs that do not conform to the edge condition at the truncated edge of each subdomain and provide a minor overlap between the cbfs in adjacent subdomains as a result the cbfs preserve the continuity of the surface current across the subdomain interfaces thereby circumventing the need to use separate ldquoconnectionrdquo basis functions

an efficient estimator for locally stationary gaussian long memory processes this paper addresses the estimation of locally stationary long range dependent processes a methodology that allows the statistical analysis of time series data exhibiting both nonstationarity and strong dependency a time varying parametric formulation of these models is introduced and a whittle likelihood technique is proposed for estimating the parameters involved large sample properties of these whittle estimates such as consistency normality and efficiency are established in this work furthermore the finite sample behavior of the estimators is investigated through monte carlo experiments as a result from these simulations we show that the estimates behave well even for relatively small sample sizes

smoothing spline anova for time dependent spectral analysis in this article we propose a smoothing spline anova model ss anova to estimate and to make inference on the time varying log spectrum of a locally stationary process the time varying spectrum is assumed to be smooth in both time and frequency this assumption essentially turns a time frequency spectral estimation problem into a 2 dimensional surface estimation problem a smooth localized complex exponential slex basis is used to calculate the initial periodograms and a ss anova is fitted to the log periodograms this approach allows the time and frequency domains to be modeled in a unified approach and jointly estimated inference procedures such as confidence intervals and hypothesis tests proposed for the ss anova can be adopted for the time varying spectrum because of the smoothness assumption of the underlying spectrum once we have the estimates on a time frequency grid we can calculate the estimate at any given time and frequency this leads to a high computational efficiency because for

functional mixed effects spectral analysis in many experiments time series data can be collected from multiple units and multiple time series segments can be collected from the same unit this article introduces a mixed effects cramer spectral representation which can be used to model the effects of design covariates on the second order power spectrum while accounting for potential correlations among the time series segments collected from the same unit the transfer function is composed of a deterministic component to account for the population average effects and a random component to account for the unit specific deviations the resulting log spectrum has a functional mixed effects representation where both the fixed effects and random effects are functions in the frequency domain it is shown that when the replicate specific spectra are smooth the log periodograms converge to a functional mixed effects model a data driven iterative estimation procedure is offered for the periodic smoothing spline estimation of the fixed effects penalized estimation of the functional covariance of the random effects and unit specific random effects prediction via the best linear unbiased predictor

dimensionality of local minimizers of the interaction energy in this work we consider local minimizers in the topology of transport distances of the interaction energy associated with a repulsive attractive potential we show how the dimensionality of the support of local minimizers is related to the repulsive strength of the potential at the origin

contractions in the 2 wasserstein length space and thermalization of granular media an algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions this rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite dimensional manifold an abstract theory is developed for gradient flows in length spaces which shows how degenerate convexity or even non convexity if uniformly controlled will quantify contractivity limit expansivity of the flow

an iteration free mom approach based on excitation independent characteristic basis functions for solving large multiscale electromagnetic scattering problems we describe a numerically efficient strategy for solving a linear system of equations arising in the method of moments for solving electromagnetic scattering problems this novel approach termed as the characteristic basis function method cbfm is based on utilizing characteristic basis functions cbfs special functions defined on macro domains blocks that include a relatively large number of conventional sub domains discretized by using triangular or rectangular patches use of these basis functions leads to a significant reduction in the number of unknowns and results in a substantial size reduction of the mom matrix this in turn enables us to handle the reduced matrix by using a direct solver without the need to iterate in addition the paper shows that the cbfs can be generated by using a sparse representation of the impedance matrix resulting in lower computational cost and that in contrast to the iterative techniques multiple excitations can be handled with only a small overhead another important attribute of the cbfm is that it is readily parallelized numerical results that demonstrate the accuracy and time efficiency of the cbfm for several representative scattering problems are included in the paper

infinite time aggregation for the critical patlak keller segel model in ℝ2 we analyze the two dimensional parabolic elliptic patlak keller segel model in the whole euclidean space r2 under the hypotheses of integrable initial data with finite second moment and entropy we first show local in time existence for any mass of free energy solutions namely weak solutions with some free energy estimates we also prove that the solution exists as long as the entropy is controlled from above the main result of the paper is to show the global existence of free energy solutions with initial data as before for the critical mass 8 actually we prove that solutions blow up as a delta dirac at the center of mass when t keeping constant their second moment at any time furthermore all moments larger than 2 blow up as t if initially bounded

convergence of the mass transport steepest descent scheme for the subcritical patlak keller segel model variational steepest descent approximation schemes for the modified patlak keller segel equation with a logarithmic interaction kernel in any dimension are considered we prove the convergence of the suitably interpolated in time implicit euler scheme defined in terms of the euclidean wasserstein distance associated with this equation for subcritical masses as a consequence we recover the recent result about the global in time existence of weak solutions to the modified patlak keller segel equation for the logarithmic interaction kernel in any dimension in the subcritical case moreover we show how this method performs numerically in dimension one in this particular case this numerical scheme corresponds to a standard implicit euler method for the pseudoinverse of the cumulative distribution function we demonstrate its capabilities to reproduce the blow up of solutions for supercritical masses easily without the need of mesh refinement

bayesian confidence intervals for smoothing splines abstract the frequency properties of wahba s bayesian confidence intervals for smoothing splines are investigated by a large sample approximation and by a simulation study when the coverage probabilities for these pointwise confidence intervals are averaged across the observation points the average coverage probability acp should be close to the nominal level from a frequency point of view this agreement occurs because the average posterior variance for the spline is similar to a consistent estimate of the average squared error and because the average squared bias is a modest fraction of the total average squared error these properties are independent of the bayesian assumptions used to derive this confidence procedure and they explain why the acp is accurate for functions that are much smoother than the sample paths prescribed by the prior this analysis accounts for the choice of the smoothing parameter bandwidth using cross validation in the case of natural splines an adaptive method for avo

fitting time series models to nonstationary processes a general minimum distance estimation procedure is presented for nonstationary time series models that have an evolutionary spectral representation the asymptotic properties of the estimate are derived under the assumption of possible model misspecification for autoregressive processes with time varying coefficients the estimate is compared to the least squares estimate furthermore the behavior of estimates is explained when a stationary model is fitted to a nonstationary process

multilevel fast adaptive cross approximation algorithm with characteristic basis functions this paper presents a multilevel fast adaptive cross approximation mlfaca algorithm for accelerated iterative solution of the method of moments mom matrix equation for electrically large targets the mlfaca compresses the impedance submatrices between well separated blocks into products of sparse matrices constructed with the aid of the fast adaptive cross sampling facs scheme and the butterfly algorithm as a result the mlfaca can reduce both the computational time and the storage of the mom to mathbf o mathbf n mathbf log mathbf 2 text n where mathbf n is the number of the rao wilton glisson rwg basis functions in the analyzed target meanwhile the mlfaca maintains the adaptive and kernel independent properties furthermore the characteristic basis function method cbfm is employed to decrease the size of the outer matrices of the mlfaca to further reduce the storage and iteration time numerical results are presented to demonstrate the advantages of the proposed method including a successful solution of a scattering problem involving 10 861 668 rwg basis functions

comparing tongue shapes from ultrasound imaging using smoothing spline analysis of variance ultrasound imaging of the tongue is increasingly common in speech production research however there has been little standardization regarding the quantification and statistical analysis of ultrasound data in linguistic studies researchers may want to determine whether the tongue shape for an articulation under two different conditions e g consonants in word final versus word medial position is the same or different this paper demonstrates how the smoothing spline anova ss anova can be applied to the comparison of tongue curves gu smoothing spline anova models springer new york 2002 the ss anova is a technique for determining whether or not there are significant differences between the smoothing splines that are the best fits for two data sets being compared if the interaction term of the ss anova model is statistically significant then the groups have different shapes since the interaction may be significant even if only a small section of the curves are different i e the tongue root is the same but the tip of one group is raised bayesian confidence intervals are used to determine which sections of the curves are statistically different ss anovas are illustrated with some data comparing obstruents produced in word final and word medial coda position

on optimization problems with prescribed rearrangements on considere certains resultats concernant des fonctions avec des distributions imposees et des prroblemes d optimisation qui y sont relies

smoothing spline anova for exponential families with application to the wisconsin epidemiological study of diabetic retinopathy the 1994 neyman memorial lecture let y i i 1 n be independent observations with the density of y i of the form h y i f i exp y i f i b f i c y i where b and c are given functions and b is twice continuously differentiable and bounded away from 0 let i t f t i where t t 1 t d t 1 t d t the t are measurable spaces of rather general form and f is an unknown function on t with some assumed smoothness properties given y i t i i 1 n it is desired to estimate f t for t in some region of interest contained in t we develop the fitting of smoothing spline anova models to this data of the form f t c f t f t t the components of the decomposition satisfy side conditions which generalize the usual side conditions for parametric anova the estimate of f is obtained as the minimizer in an appropriate function space of l y f j f j f where l y f is the negative log likelihood of y y 1 y n given f the j j are quadratic penalty functionals and the anova decomposition is terminated in some manner there are five major parts required to turn this program into a practical data analysis tool 1 methods for deciding which terms in the anova decomposition to include model selection 2 methods for choosing good values of the smoothing parameters 3 methods for making confidence statements concerning the estimate 4 numerical algorithms for the calculations and finally 5 public software in this paper we carry out this program relying on earlier work and filling in important gaps the overall scheme is applied to bernoulli data from the wisconsin epidemiologic study of diabetic retinopathy to model the risk of progression of diabetic retinopathy as a function of glycosylated hemoglobin duration of diabetes and body mass index it is believed that the results have wide practical application to the analysis of data from large epidemiologic studies

tensor product space anova models to deal with the curse of dimensionality in high dimensional nonparametric problems we consider using tensor product space anova models which extend the popular additive models and are able to capture interactions of any order the multivariate function is given an anova decomposition that is it is expressed as a constant plus the sum of functions of one variable main effects plus the sum of functions of two variables two factor interactions and so on we assume the interactions to be in tensor product spaces we show in both regression and white noise settings the optimal rate of convergence for the tps anova model is within a log factor of the one dimensional optimal rate and that the penalized likelihood estimator in tps anova achieves this rate of convergence the quick optimal rate of the tps anova model makes it very preferable in high dimensional function estimation many properties of the tensor product space of sobolev hilbert spaces are also given

adaptspec adaptive spectral estimation for nonstationary time series we propose a method for analyzing possibly nonstationary time series by adaptively dividing the time series into an unknown but finite number of segments and estimating the corresponding local spectra by smoothing splines the model is formulated in a bayesian framework and the estimation relies on reversible jump markov chain monte carlo rjmcmc methods for a given segmentation of the time series the likelihood function is approximated via a product of local whittle likelihoods thus no parametric assumption is made about the process underlying the time series the number and lengths of the segments are assumed unknown and may change from one mcmc iteration to another the frequentist properties of the method are investigated by simulation and applications to electroencephalogram and the el nino southern oscillation phenomenon are described in detail

semiparametric analysis of variance with tensor product thin plate splines we consider fitting multivariate models to response data based on analysis of variance anova like decompositions of functions of several variables f t 1 t d c f t f t t a theory for fitting some components of these models with polynomial smoothing splines exists when each t is in a subset of the real line in this case the various estimated components turn out to be certain tensor sums and products of polynomial splines this approach may not be natural when one or more of the variables are geographic in particular where nature does not know north from east

nonparametric spectral density estimation using penalized whittle likelihood abstract the penalized likelihood approach is not well developed in time series analysis even though it has been applied successfully in a number of nonparametric function estimation problems chow and grenander proposed a penalized likelihood type approach to the nonparametric estimation of the spectral density of gaussian processes in this article this estimator is extended to more general stationary processes its practical implementation is developed in some detail and some asymptotic rates of convergence are established its performance is also compared to more widely used alternatives in the field a computational algorithm involving an iterative least squares initialized by the log periodogram is first developed then motivated by an asymptotic linearization an estimator of the integrated squared error between the estimated and true log spectral densities is proposed from this a data dependent procedure for selection of the amount of smoothing is constructed the methodology is illustrated

function on function linear regression by signal compression abstractwe consider functional linear regression models with a functional response and multiple functional predictors with the goal of finding the best finite dimensional approximation to the signal part of the response function defining the integrated squared correlation coefficient between a random variable and a random function we propose to solve a penalized generalized functional eigenvalue problem whose solutions satisfy that projections on the original predictors generate new scalar uncorrelated variables and these variables have the largest integrated squared correlation coefficient with the signal function with these new variables we transform the original function on function regression model to a function on scalar regression model whose predictors are uncorrelated and estimate the model by penalized least square method this method is also extended to models with both multiple functional and scalar predictors we provide the asymptotic consistency and the corresponding convergence rates

multiscale compressed block decomposition for fast direct solution of method of moments linear system the multiscale compressed block decomposition algorithm ms cbd is presented for highly accelerated direct non iterative solution of electromagnetic scattering and radiation problems with the method of moments mom the algorithm is demonstrated to exhibit n2 computational complexity and storage requirements scaling with n1 5 for electrically large objects several numerical examples illustrate the efficiency of the method in particular for problems with multiple excitation vectors the largest problem presented in this paper is the monostatic rcs of the nasa almond at 50 ghz for one thousand incidence angles discretized using 442 089 rwg basis functions being entirely algebraic ms cbd is independent of the greens function of the problem

preventing blow up in a chemotaxis model abstract this paper deals with a chemotactic model of keller segel type the main feature of the keller segel model is the possibility of blow up of solutions in a finite time to eliminate the possibility of blow up a modified version of keller segel model is introduced the blow up control relies on the presence of a pressure function which increases faster than a logarithm for high enough cells densities for such a pressure function the solutions cannot blow up in a finite time some other conditions are introduced to ensure the global boundedness