a chebyshev based rectangular polar integral solver for scattering by general geometries described by non overlapping patches this paper introduces a high order accurate strategy for integration of singular kernels and edge singular integral densities that appear in the context of boundary integral equation formulations of the problem of acoustic scattering in particular the proposed method is designed for use in conjunction with geometry descriptions given by a set of arbitrary non overlapping logically quadrilateral patches which makes the algorithm particularly well suited for treatment of cad generated geometries fejer s first quadrature rule is incorporated in the algorithm to provide a spectrally accurate method for evaluation of contributions from far integration regions while highly accurate precomputations of singular and near singular integrals over certain surface patches together with two dimensional chebyshev transforms and suitable surface varying rectangular polar changes of variables are used to obtain the contributions for singular and near singular interactions the overall integration method is then used in conjunction with the linear algebra solver gmres to produce solutions for sound soft open and closed surface scattering obstacles including an application to an aircraft described by means of a cad representation the approach is robust fast and highly accurate use of a few points per wavelength suffices for the algorithm to produce far field accuracies of a fraction of a percent and slight increases in the discretization densities give rise to significant accuracy improvements

nonparametric estimation of conditional quantile functions in the presence of irrelevant covariates abstract allowing for the existence of irrelevant covariates we study the problem of estimating a conditional quantile function nonparametrically with mixed discrete and continuous data we estimate the conditional quantile regression function using the check function based kernel method and suggest a data driven cross validation cv approach to simultaneously determine the optimal smoothing parameters and remove the irrelevant covariates when the number of covariates is large we first use a screening method to remove the irrelevant covariates and then apply the cv criterion to those that survive the screening procedure simulations and an empirical application demonstrate the usefulness of the proposed methods

some aspects of the spline smoothing approach to non parametric regression curve fitting non parametric regression using cubic splines is an attractive flexible and widely applicable approach to curve estimation although the basic idea was formulated many years ago the method is not as widely known or adopted as perhaps it should be the topics and examples discussed in this paper are intended to promote the understanding and extend the practicability of the spline smoothing methodology particular subjects covered include the basic principles of the method the relation with moving average and other smoothing methods the automatic choice of the amount of smoothing and the use of residuals for diagnostic checking and model adaptation the question of providing inference regions for curves and for relevant properties of curves is approached via a finite dimensional bayesian formulation

splines in statistics abstract this is a survey article that attempts to synthesize a broad variety of work on splines in statistics splines are presented as a nonparametric function estimating technique after a general introduction to the theory of interpolating and smoothing splines splines are treated in the nonparametric regression setting the method of cross validation for choosing the smoothing parameter is discussed and the general multivariate regression surface estimation problem is addressed an extensive discussion of splines as nonparametric density estimators is followed by a discussion of their role in time series analysis a comparison of the spline and isotonic regression methodologies leads to a formulation of a hybrid estimator the closing section provides a brief overall summary and formulates a number of open unsolved problems relating to splines in statistics

a two stage filter for smoothing multivariate noisy data on unstructured grids abstract experimental data as well as numerical simulations are very often affected by noise random fluctuations that distort the final output or the intermediate products of a numerical process in this paper a new method for smoothing data given on nonstructured grids is proposed it takes advantage of the smoothing properties of kernel weighted averaging and least squares techniques the weighted averaging is performed following a shepard like procedure where gaussian kernels are employed while least squares fitting is reduced to the use of very few basis functions so as to improve smoothness though at the price of interpolation accuracy once we have defined an n point grid and want to make a smoothed fit at a given grid point this method reduces to consideration of all m point stencils for a given value of m where m n that include that point and to make a least squares fitting for that particular point in each of those stencils finally the various results thus obtained are weight averaged the weights being inversely proportional to the distance of the point to the middle of the stencil then this process is repeated for all the grid points so as to obtain the smoothing of the input function though this method is generalized for the multivariate case one two and five dimensional test cases are shown as examples of the performance of this method

local polynomial variance function estimation the conditional variance function in a heteroscedastic nonparametric regression model is estimated by linear smoothing of squared residuals attention is focused on local polynomial smoothers both the mean and variance functions are assumed to be smooth but neither is assumed to be in a parametric family the biasing effect of preliminary estimation of the mean is studied and a degrees of freedom correction of bias is proposed the corrected method is shown to be adaptive in the sense that the variance function can be estimated with the same asymptotic mean and variance as if the mean function were known a proposal is made for using standard bandwidth selectors for estimating both the mean and variance functions the proposal is illustrated with data from the lidar method of measuring atmospheric pollutants and from turbulence model computations

adapting to unknown sparsity by controlling the false discovery rate we attempt to recover an n dimensional vector observed in white noise where n is large and the vector is known to be sparse but the degree of sparsity is unknown we consider three different ways of defining sparsity of a vector using the fraction of nonzero terms imposing power law decay bounds on the ordered entries and controlling the lp norm for p small we obtain a procedure which is asymptotically minimax for l r loss simultaneously throughout a range of such sparsity classes the optimal procedure is a data adaptive thresholding scheme driven by control of the false discovery rate fdr fdr control is a relatively recent innovation in simultaneous testing ensuring that at most a certain fraction of the rejected null hypotheses will correspond to false rejections in our treatment the fdr control parameter qn also plays a determining role in asymptotic minimaxity if q lim qn 0 1 2 and also qn log n we get sharp asymptotic minimaxity simultaneously over a wide range of sparse parameter spaces and loss functions on the other hand q lim qn 1 2 1 forces the risk to exceed the minimax risk by a factor growing with q to our knowledge this relation between ideas in simultaneous inference and asymptotic decision theory is new our work provides a new perspective on a class of model selection rules which has been introduced recently by several authors these new rules impose complexity penalization of the form 2 log potential model size actual model size we exhibit a close connection with fdr controlling procedures under stringent control of the false discovery rate

goodness of fit tests for kernel regression with an application to option implied volatilities this paper proposes a test of a restrictedspeci cation of regression basedon comparing residual sum of squares from kernel regression our main case is where both the restrictedspeci cation andthe general mod el are nonparametric with our test equivalently viewed as a test of dimension reduction we discuss practical features of implementing the test andvariations applicable to testing parametric mod els as the null hypothesis or semiparametric models that depend on a nite parameter vector as well as unknown functions we apply our testing procedure to option prices we reject a parametric version of the black scholes formula but fail to reject a semiparametric version against a general nonparametric regression 2001 elsevier science s a all rights reserved jel classi cation c12 c14

the optimal p version approximation of singularities on polyhedra in the boundary element method we consider elliptic boundary value problems on three dimensional polyhedral domains we describe the three types of singular components that arise in the solution edge vertex and edge vertex singularities we analyze the approximation of the traces of each of each of these different types of singularities by polynomial subspaces on the boundary as the polynomial degree p tends to infinity the p version we establish asymptotic rates of convergence that are optimal in the h t norm over the boundary for 0 leq t leq 1 we apply these results to a galerkin boundary element method bem formulation for a model neumann problem obtaining the optimal convergence rate for the p version bem over polyhedral domains

using medical malpractice data to predict the frequency of claims a study of poisson process models with random effects abstract i use the florida state data base 1975 1987 of settled malpractice claims to develop poisson process models for the frequency of claims filed against individual physicians these models incorporate random effects and covariates that represent physician attributes and are natural generalizations of the negative binomial model that is typically used to study claims frequency i predict claims frequencies during 1981 1982 using models that are selected and estimated from claims data during 1975 1980 and then compare these predictions to the actual frequencies

pullbacks of saito kurokawa lifts pullbacks of siegel eisenstein series have been studied by garrett 17 18 bocherer 6 7 heim 26 and play a key role in the proof of the algebraicity of critical values of certain automorphic l functions more generally one might consider pullbacks of siegel cusp forms for example ikeda 30 gave a conjectural formula for pullbacks of ikeda lifts 29 in terms of critical values of l functions for spn gl2 also the gross prasad conjecture 22 23 8 27 8 would relate pullbacks of siegel cusp forms of degree 2 to central critical values of l functions for gsp2 gl2 gl2 indeed bocherer furusawa and schulze pillot 8 gave an explicit formula for pullbacks of yoshida lifts 57 in this paper we give an explicit formula for pullbacks of saito kurokawa lifts and prove the algebraicity of central critical values of certain l functions for sp1 gl2 to be precise let be an odd positive integer let f s2 sl2 z be a normalized hecke eigenform and h s 1 2 0 4 a hecke eigenform associated to f by the shimura correspondence let f s 1 sp2 z be the saito kurokawa lift of h for each normalized hecke eigenform g s 1 sl2 z we consider the period integral f h h g g given by f h h g g

spline smoothing the equivalent variable kernel method on considere une approche spline pour la regression non parametrique et l estimation de courbe on montre que dans un certain sens le lissage spline correspond approximativement au lissage par une methode du noyau avec une largeur de bande dependant de la densite locale des points du plan de regression

from fixed x to random x regression bias variance decompositions covariance penalties and prediction error estimation in statistical prediction classical approaches for model selection and model evaluation based on covariance penalties are still widely used most of the literature on this topic is based on what w

on the gamma factor of the triple l function i introduction the study of the triple l function began with garrett 2 from a representation theoretic point of view piatetski shapiro and rallis 9 and the author 6 defined the archimedean or nonarchimedean l factor as the greatest common divisor gcd of local integrals the purpose of this paper is to prove that the archimedean gcd l factor agrees with the expected l factor up to invertible functions if the local representation comes from a cuspidal automorphic representation this theorem follows from the local functional equation by formal argument except when the representation is unramified to treat the unramified case we carry out the explicit calculation of the unramified local integral stimulated by stade 12 we make use of a hypergeometric function 3f2 and its two term relations and three term relation we also need a theorem on some infinite integral involving bessel functions proved by bailey 1 in 1936 the key lemma is the following see lemma 2 4

directional sparsity in optimal control of partial differential equations we study optimal control problems in which controls with certain sparsity patterns are preferred for time dependent problems the approach can be used to find locations for control devices that allow controlling the system in an optimal way over the entire time interval the approach uses a nondifferentiable cost functional to implement the sparsity requirements additionally bound constraints for the optimal controls can be included we study the resulting problem in appropriate function spaces and present two solution methods of newton type based on different formulations of the optimality system using elliptic and parabolic test problems we research the sparsity properties of the optimal controls and analyze the behavior of the proposed solution algorithms

how many variables should be entered in a regression equation abstract the optimal number of regressors is determined to minimize mean squared prediction error and is shown to be a small fraction of the number of data points as the number of regressors grows large the sp criterion provides an asymptotically optimal rule for the number of variables to enter

data compression and histograms in this paper the relationship between code length and the selection of the number of bins for a histogram density is considered for a sequence of iid observations on 0 1 first we use a shortest code length criterion to select the number of bins for a histogram a uniform almost sure asymptotic expansion for the code length is given and it is used to prove the asymptotic optimality of the selection rule in addition the selection rule is consistent if the true density is uniform 0 1 secondly we deal with the problem what is the best achievable average code length with underlying density functionf minimax lower bounds are derived for the average code length over certain smooth classes of underlying densitiesf for the smooth class with bounded first derivatives the rate in the lower bound is shown to be achieved by a code based on a sequence of histograms whose number of bins is changed predictively moreover this best code can be modified to ensure that the almost sure version of the code length has asymptotically the same behavior as its expected value i e the average code length

linear smoothers and additive models we study linear smoothers and their use in building nonparametric regression models in the first part of this paper we examine certain aspects of linear smoothers for scatterplots examples of these are the running mean and running line kernel and cubic spline smoothers the eigenvalue and singular value decompositions of the corresponding smoother matrix are used to describe qualitatively a smoother and several other topics such as the number of degrees of freedom of a smoother are discussed in the second part of the paper we describe how linear smoothers can be used to estimate the additive model a powerful nonparametric regression model using the backfitting algorithm we show that backfitting is the gauss seidel iterative method for solving a set of normal equations associated with the additive model we provide conditions for consistency and nondegeneracy and prove convergence for the backfitting and related algorithms for a class of smoothers that includes cubic spline smoothers

characteristics of the process zone at sharp notch roots the classical williams solution for the state of stress at the tip of a semi infinite notch is re visited and the two term singular solution re written in a form making the mode mixity and load magnitude explicit this is used to show that for a 270 solid angle the majority of notch problems exhibit a process zone which is entirely or substantially mode i in character which in turn means that the notch strength may practically be governed by a single elastic parameter a method for finding the practical limit on the load and stress intensity ratio where this holds is described

correlation and high dimensional consistency in pattern recognition abstract classical discriminant analysis breaks down when the feature vectors are of extremely high dimension for example when the basic observation is a random function observed over a fine grid alternative methods have been developed assuming a simplified form for the covariance structure we analyze the high dimensional asymptotics of some of these methods emphasizing the effects of correlations such as occur when the baseline is random for instance the euclidean distance classifier which has been proposed for generic use in high dimensional classification problems is dimensionally inconsistent under a simple repeated measurement model we provide exponential bounds for the error rates of several classifiers we develop new dimensionally consistent methods to deal with the effects of correlation in high dimensional problems

the l 1 method for robust nonparametric regression abstract consider the problem of estimating the regression function underlying a set of data that is contaminated by a heavy tailed error distribution the two standard approaches to such a problem are each flawed robust parametric least squares is appropriate only if there is good reason to believe that the underlying function has some particular form whereas most nonparametric regression methods are asymptotically equivalent to kernel regression methods which are not resistant against outliers existing algorithms for robustifying nonparametric regression procedures use either nonlinear optimization of an influence function or iterative solution of local polynomial fitting using reweighted least squares neither of these two approaches combines computational ease with asymptotic theoretical results furthermore application of the robust procedure has been limited almost exclusively to the case of a single explanatory variable with the response variable in this article a new hybrid method is propose

general edge asymptotics of solutions of second order elliptic boundary value problems i this is the first of two papers in which we study the singularities of solutions of second order linear elliptic boundary value problems at the edges of piecewise analytic domains in 3 when the opening angle at the edge is variable there appears the phenomenon of crossing of the exponents of singularities for this case we introduce the appropriate combinations of the simple tensor product singularities that allow us to give estimates in ordinary and weighted sobolev spaces for the regular part of the solution and for the coefficients of the singularities these combinations appear in a natural way as sections of an analytic bundle above the edge their behaviour is described with the help of divided differences of powers of the distance to the edge the class of operators considered includes second order elliptic operators with analytic complex valued coefficients with mixed dirichlet neumann or oblique derivative conditions with our description of the singularities we are able to remove some restrictive hypotheses that were previously made in other works in this first part we prove the basic facts in a simplified framework nevertheless the tools we use are essentially the same in the general situation

a survey of the maximum principles for optimal control problems with state constraints this paper gives a survey of the various forms of pontryagin s maximum principle for optimal control problems with state variable inequality constraints the relations between the different sets of optimality conditions arising in these forms are shown furthermore the application of these maximum principle conditions is demonstrated by solving some illustrative examples

on maass lifts and the central critical values of triple product l functions we express certain period integrals of maass lifts which appear in the gross prasad conjecture in terms of the central critical values of triple product l functions in the imbalanced case

barrier methods for optimal control problems with convex nonlinear gradient state constraints in this paper we are concerned with the application of interior point methods in function space to gradient constrained optimal control problems governed by partial differential equations we will derive existence of solutions together with first order optimality conditions afterwards we show continuity of the central path together with convergence rates depending on the interior point parameter

regularity of the solutions for elliptic problems on nonsmooth domains in r3 part 2 regularity in neighborhoods of edges this paper is the second in a series of three devoted to the analysis of the regularity of solutions of elliptic problems on nonsmooth domains in 3 the present paper concentrates on the regularity of solutions of the poisson equation in neighbourhoods of edges of a polyhedral domain in the framework of the weighted sobolev spaces and countably normed spaces these results can be generalised to elliptic problems arising from mechanics and engineering for instance the elasticity problem on polyhedral domains hence the results are not only important to understand comprehensively the qualitative and quantitative aspects of the behaviours of the solution and its derivatives of all orders in neighbourhoods of edges but also essential to design an effective computation and analyse the optimal convergence of the finite elements solutions for these problems

weighted norm least squares finite element method for poisson equation in a polyhedral domain this paper concerns poisson equation in a polyhedral domain with corners and edges we apply the least squares finite element method to the reformulated first order system of poisson equation to overcome the difficulties from boundary singularities a weighted norm technique is used to define the least squares functional the method prevents the loss of global accuracy numerical simulations are given to demonstrate the theoretical estimates

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

model free variable selection computing power has encouraged the modelling of data sets of ever increasing size data mining applications in finance marketing and bioinformatics are obvious examples a limitation of nearly all existing variable selection methods is the need to specify the correct model before selection when the number of predictors is large model formulation and validation can be difficult or even infeasible on the basis of the theory of sufficient dimension reduction we propose a new class of model free variable selection approaches the methods proposed assume no model of any form require no nonparametric smoothing and allow for general predictor effects the efficacy of the methods proposed is demonstrated via simulation and an empirical example is given

variable selection in nonparametric regression with continuous covariates in a nonparametric regression setup where the covariates are continuous the problem of estimating the number of covariates will be discussed in this paper the kernel method is used to estimate the regression function and the selection criterion is based on minimizing the cross validation estimate of the mean squared prediction error we consider choosing both the bandwidth and the number of covariates based on the data unlike the case of linear regression it turns out that the selection is consistent and efficient even when the true model has only a finite number of covariates in addition we also observe the curse of dimensionality at work

hierarchical testing of variable importance a frequently encountered challenge in high dimensional regression is the detection of relevant variables variable selection suffers from instability and the power to detect relevant variables is typically low if predictor variables are highly correlated when taking the multiplicity of the testing problem into account the power diminishes even further to gain power and insight it can be advantageous to look for influence not at the level of individual variables but rather at the level of clusters of highly correlated variables we propose a hierarchical approach variable importance is first tested at the coarsest level corresponding to the global null hypothesis the method then tries to attribute any effect to smaller subclusters or even individual variables the smallest possible clusters which still exhibit a significant influence on the response variable are retained it is shown that the proposed testing procedure controls the familywise error rate at a prespecified level simultaneously over all resolution levels the method has power comparable to the bonferroni holm procedure on the level of individual variables and dramatically larger power for coarser resolution levels the best resolution level is selected adaptively

local discriminative learning for pattern recognition abstract local discriminative learning methods approximate a target function a posteriori class probability function directly by partitioning the feature space into a set of local regions and appropriately modeling a simple input output relationship function in each one this paper presents a new method for judiciously partitioning the input feature space in order to accurately represent the target function the method accomplishes this by approximating not only the target function itself but also its derivatives as such the method partitions the input feature space along those dimensions for which the class probability function changes most rapidly thus minimizing bias the efficacy of the method is validated using a variety of simulated and real world data

adaptive prediction and estimation in linear regression with infinitely many parameters the problem of adaptive prediction and estimation in the stochastic linear regression model with infinitely many parameters is considered we suggest a prediction method that is sharp asymptotically minimax adaptive over ellipsoids in 2 the method consists in an application of blockwise stein s rule with weakly geometrically increasing blocks to the penalized least squares fits of the first n coefficients to prove the results we develop oracle inequalities for a sequence model with correlated data

some diagnostics for binary logistic regression via smoothing summary the paper discusses some diagnostic tools for binary logistic regression which use smoothing techniques smoothed binary data are employed to devise a battery of diagnostic plots from simple procedures which indicate only the adequacy or inadequacy of a maximum likelihood logistic fit to partial residual plots and delta local deviance plots which reveal the type of model inadequacy suggesting perhaps the addition of nonlinear terms or interactions properties of the methods are studied by simulation the diagnostic tools are illustrated on a set of data in which the probability of having telephone service is related to the demographic variables income and education

bandwidth choice for nonparametric regression this paper is concerned with the problem of choosing a bandwidth parameter for nonparametric regression we analyze a tapered fourier series estimate and discuss the relationship of this estimate to a kernel estimate we first consider a method based on an unbiased estimate of mean square error and show that the bandwidth thus chosen is asymptotically optimal other methods are examined as well and are shown to be asymptotically equivalent a small simulation shows however that for small or moderate sample size the methods perform quite differently

conditional predictive inference post model selection we give a finite sample analysis of predictive inference procedures after model selection in regression with random design the analysis is focused on a statistically challenging scenario where the number of potentially important explanatory variables can be infinite where no regularity conditions are imposed on unknown parameters where the number of explanatory variables in a good model can be of the same order as sample size and where the number of candidate models can be of larger order than sample size the performance of inference procedures is evaluated conditional on the training sample under weak conditions on only the number of candidate models and on their complexity and uniformly over all data generating processes under consideration we show that a certain prediction interval is approximately valid and short with high probability in finite samples in the sense that its actual coverage probability is close to the nominal one and in the sense that its length is close to the length of an infeasible interval that is constructed by actually knowing the best candidate model similar results are shown to hold for predictive inference procedures other than prediction intervals like for example tests of whether a future response will lie above or below a given threshold

extracting edge flux intensity functions for the laplacian the solution to the laplace operator in three dimensional domains in the vicinity of straight edges is presented as an asymptotic expansion involving eigenpairs with their coefficients called edge flux intensity functions efifs the eigenpairs are identical to their two dimensional counterparts over a plane perpendicular to the edge extraction of efifs however cannot be obtained in a straightforward manner over this two dimensional plane a method based on l 2 projection and richardson extrapolation is presented for point wise extraction of efifs from p finite element solutions and illustrated by examples a similar but more efficient method based on energy projection for extracting efifs is proposed

admissible variable selection procedures when fitting regression models by least squares for prediction given data with a single dependent variable arising from a normal linear regression model a variable selection procedure completely specifies a least squares fit by choosing the subset of the independent variables to include in the model for loss equal to squared error of prediction we prove that all variable selection procedures are admissible for choosing among least squares fits of the regression model

from stein s unbiased risk estimates to the method of generalized cross validation this paper concerns the method of generalized cross validation gcv a promising way of choosing between linear estimates based on stein estimates and the associated unbiased risk estimates stein 1981 a new approach to gcv is developed many consistency results are obtained for the cross validated steinized estimates in the contexts of nearest neighbor nonparametric regression model selection ridge regression and smoothing splines moreover the associated stein s unbiased risk estimate is shown to be uniformly consistent in assessing the true loss not the risk consistency properties are examined as well when the sampling error is unknown finally we propose a variant of gcv to handle the case that the dimension of the raw data is known to be greater than that of their expected values

some comments on cp i study the typical configuration of a cp plot when the number of variables in the regression problem is large and there are many weak effects i show that a particular configuration that is very commonly seen can arise in a simple way i give a formula by means of which the risk incurred by the minimum cp rule can be estimated

an adaptable k nearest neighbors algorithm for mmse image interpolation we propose an image interpolation algorithm that is nonparametric and learning based primarily using an adaptive k nearest neighbor algorithm with global considerations through markov random fields the empirical nature of the proposed algorithm ensures image results that are data driven and hence reflect ldquoreal worldrdquo images well given enough training data the proposed algorithm operates on a local window using a dynamic k nearest neighbor algorithm where k differs from pixel to pixel small for test points with highly relevant neighbors and large otherwise based on the neighbors that the adaptable k provides and their corresponding relevance measures a weighted minimum mean squared error solution determines implicitly defined filters specific to low resolution image content without yielding to the limitations of insufficient training additionally global optimization via single pass markov approximations similar to cited nearest neighbor algorithms provides additional weighting for filter generation the approach is justified in using a sufficient quantity of training per test point and takes advantage of image properties for in depth analysis we compare to existing methods and draw parallels between intuitive concepts including classification and ideas introduced by other nearest neighbor algorithms by explaining manifolds in low and high dimensions

locally weighted polynomial regression parameter choice and application to forecasts of the great salt lake 1 relationships between hydrologic variables are often nonlinear usually the functional form of such a relationship is not known a priori a multivariate nonparametric regression methodology is provided here for approximating the underlying regression function using locally weighted polynomials locally weighted polynomials consider the approximation of the target function through a taylor series expansion of the function in the neighborhood of the point of estimate cross validatory procedures for the selection of the size of the neighborhood over which this approximation should take place and for the order of the local polynomial to use are provided and shown for some simple situations the utility of this nonparametric regression approach is demonstrated through an application to nonparametric short term forecasts of the biweekly great salt lake volume blind forecasts up to 1 year in the future using the 1847 2004 time series of the great salt lake are presented

on measuring and correcting the effects of data mining and model selection abstract in the theory of linear models the concept of degrees of freedom plays an important role this concept is often used for measurement of model complexity for obtaining an unbiased estimate of the error variance and for comparison of different models i have developed a concept of generalized degrees of freedom gdf that is applicable to complex modeling procedures the definition is based on the sum of the sensitivity of each fitted value to perturbation in the corresponding observed value the concept is nonasymptotic in nature and does not require analytic knowledge of the modeling procedures the concept of gdf offers a unified framework under which complex and highly irregular modeling procedures can be analyzed in the same way as classical linear models by using this framework many difficult problems can be solved easily for example one can now measure the number of observations used in a variable selection process different modeling procedures such as a tree based regression and a

acoustic articulatory mapping in vowels by locally weighted regression a method for mapping between simultaneously measured articulatory and acoustic data is proposed the method uses principal components analysis on the articulatory and acoustic variables and mapping between the domains by locally weighted linear regression or loess cleveland w s 1979 j am stat assoc 74 829 836 the latter method permits local variation in the slopes of the linear regression assuming that the function being approximated is smooth the methodology is applied to vowels of four speakers in the wisconsin x ray microbeam speech production database with formant analysis results are examined in terms of 1 examples of forward articulation to acoustics mappings and inverse mappings 2 distributions of local slopes and constants 3 examples of correlations among slopes and constants 4 root mean square error and 5 sensitivity of formant frequencies to articulatory change it is shown that the results are qualitatively correct and that loess performs better than global regression the forward mappings show different root mean square error properties than the inverse mappings indicating that this method is better suited for the forward mappings than the inverse mappings at least for the data chosen for the current study some preliminary results on sensitivity of the first two formant frequencies to the two most important articulatory principal components are presented

regression by local fitting methods properties and computational algorithms abstract local regression is a procedure for estimating regression surfaces by the local fitting of linear or quadratic functions of the independent variables in a moving fashion that is analogous to how a moving average is computed for a time series the advantage of the methodology over the global fitting of parametric functions of the independent variables by least squares the current paradigm in regression studies is that a much wider class of regression functions can be estimated without distortion in this paper we discuss the methods their statistical properties and computational algorithms

a new method to discriminate between enzyme kinetic models abstract a novel statistical procedure s zwanzig math opsforsch statist ser statist 11 23 47 1980 is applied to discriminate between kinetic models of enzyme reactions two examples are elucidated on the basis of numerically simulated data 1 a discrimination between a michaelis menten model and a hill equation 2 b discrimination between competitive and noncompetitive inhibition of a two substrate reaction next the proposed method is applied to assess a kinetic model of the allosteric enzyme phosphofructokinase from the malarial parasite plasmodium berghei it is demonstrated that the novel procedure allows a more sensitive discrimination as it is obtained with alternative statistical tests

doubling constructions and tensor product l functions the linear case we present an integral representation for the tensor product l function of a pair of automorphic cuspidal representations one of a classical group the other of a general linear group our construction is uniform over all classical groups and is applicable to all cuspidal representations it does not require genericity the main new ideas of the construction are the use of generalized speh representations as inducing data for the eisenstein series and the introduction of a new global and local model which generalizes the whittaker model here we consider linear groups but our construction also extends to arbitrary degree metaplectic coverings this will be the topic of an upcoming work

variable selection in nonparametric regression with categorical covariates abstract this article extends the problem of variable selection to a nonparametric regression model with categorical covariates two selection criteria are considered the cross validation cv criterion and the accumulated prediction error ape criterion we find that asymptotically the cv criterion performs well only when the true model is infinite dimensional while the ape criterion is appropriate when the true model is finite dimensional this is very similar to the case of linear regression model a simulation study reveals some interesting small sample properties of these criteria to be more specific suppose that we have observations x 1 y 1 xn yn that are iid random vectors and x x 1 x 2 where the x i s are categorical we allow y to be of any type now a new observation x has arrived and we want to predict the corresponding y such a framework is more appropriate than regressions with fixed covariates in situations where the covariates are observational rather than bei

locally weighted regression an approach to regression analysis by local fitting abstract locally weighted regression or loess is a way of estimating a regression surface through a multivariate smoothing procedure fitting a function of the independent variables locally and in a moving fashion analogous to how a moving average is computed for a time series with local fitting we can estimate a much wider class of regression surfaces than with the usual classes of parametric functions such as polynomials the goal of this article is to show through applications how loess can be used for three purposes data exploration diagnostic checking of parametric models and providing a nonparametric regression surface along the way the following methodology is introduced a a multivariate smoothing procedure that is an extension of univariate locally weighted regression b statistical procedures that are analogous to those used in the least squares fitting of parametric functions c several graphical methods that are useful tools for understanding loess estimates and checking the a

a priori error estimates for optimal control problems with pointwise constraints on the gradient of the state we analyze a finite element approximation of an elliptic optimal control problem with pointwise bounds on the gradient of the state variable we derive convergence rates if the control space is discretized implicitly by the state equation in contrast to prior work we obtain these results directly from classical results for the w 1 error of the finite element projection without using adjoint information if the control space is discretized directly we first prove a regularity result for the optimal control to control the approximation error based on which we then obtain analogous convergence rates

a tree structured adaptive network for function approximation in high dimensional spaces nonlinear function approximation is often solved by finding a set of coefficients for a finite number of fixed nonlinear basis functions however if the input data are drawn from a high dimensional space the number of required basis functions grows exponentially with dimension leading many to suggest the use of adaptive nonlinear basis functions whose parameters can be determined by iterative methods the author proposes a technique based on the idea that for most of the data only a few dimensions of the input may be necessary to compute the desired output function additional input dimensions are incorporated only where needed the learning procedure grows a tree whose structure depends upon the input data and the function to be approximated this technique has a fast learning algorithm with no local minima once the network shape is fixed and it can be used to reduce the number of required measurements in situations where there is a cost associated with sensing three examples are given controlling the dynamics of a simulated planar two joint robot arm predicting the dynamics of the chaotic mackey glass equation and predicting pixel values in real images from pixel values above and to the left

an optimization approach for well targeted transcranial direct current stimulation transcranial direct current stimulation tdcs is a noninvasive brain stimulation technique which modifies neural excitability by providing weak currents through scalp electrodes the aim of this study is to introduce and analyze a novel optimization method for safe and well targeted multiarray tdcs for optimization we consider an optimal control problem for a laplace equation with neumann boundary conditions with control and pointwise gradient state constraints we prove well posedness results for the proposed methods and provide computer simulation results in a highly realistic six compartment geometry adapted hexahedral head model for discretization of the proposed minimization problem the finite element method is employed and the existence of at least one minimizer to the discretized optimization problem is shown for numerical solution of the corresponding discretized problem we employ the alternating direction method of multipliers and comprehensively examine the cortical current flow field with regard to focality target intensity and orientation the numerical results reveal that the optimized current flow fields show significantly higher focality and in most cases higher directional agreement to the target vector in comparison to standard bipolar electrode montages

optimal control of elliptic equations with pointwise constraints on the gradient of the state in nonsmooth polygonal domains this article is concerned with optimal control problems subject to a second order elliptic pde and additional pointwise constraints on the gradient of the state in particular the existence of solutions on nonsmooth polygonal or polyhedral domains is analyzed in this situation the solution operator for the pde does not provide enough regularity to state the pointwise constraint for any right hand side due to the appearance of singularities associated to the corners edges and vertices of the domain further necessary optimality conditions for the solution of the optimization problem in two and three space dimensions are derived however in the three dimensional case certain critical angles along the edges of the domain have to be circumvented in the derivation of the optimality conditions finally the derived optimality conditions are utilized to deduce additional regularity for the control variable

order selection for same realization predictions in autoregressive processes assume that observations are generated from an infinite order autoregressive ar process shibata ann statist 8 1980 147 164 considered the problem of choosing a finite order ar model allowing the order to become infinite as the number of observations does in order to obtain a better approximation he showed that for the purpose of predicting the future of an independent replicate akaike s information criterion aic and its variants are asymptotically efficient although shibata s concept of asymptotic efficiency has been widely accepted in the literature it is not a natural property for time series analysis this is because when new observations of a time series become available they are not independent of the previous data to overcome this difficulty in this paper we focus on order selection for forecasting the future of an observed time series referred to as same realization prediction we present the first theoretical verification that aic and its variants are still asymptotically elficient in the sense defined in section 4 for same realization predictions to obtain this result a technical condition easily met in common practice is introduced to simplify the complicated dependent structures among the selected orders estimated parameters and future observations in addition a simulation study is conducted to illustrate the practical implications of aic this study shows that aic also yields a satisfactory saute realization prediction in finite samples on the other hand a limitation of aic in same realization settings is pointed out it is interesting to note that this limitation of aic does not exist for corresponding independent cases

filtering out high frequencies in time series using f transform abstract in this paper we focus on application of fuzzy transform f transform to analysis of time series under the assumption that the latter can be additively decomposed into trend cycle seasonal component and noise we prove that when setting properly width of the basic functions the inverse f transform of the time series closely approximates its trend cycle this means that the f transform almost completely removes the seasonal component and noise the obtained theoretical results are demonstrated on two artificial time series whose trend cycle is precisely known and on three real time series at the same time comparison with three classical methods namely stl method ssa method and low pass butterworth filter is also provided

numerical methods for extracting edge stress intensity functions in anisotropic three dimensional domains the solution to elasticity problems in three dimensional 3 d polyhedral domains in the vicinity of an edge is represented by a family of eigen functions similar to 2 d domains complemented by shadow functions and their associated edge stress intensity functions esifs which are functions along the edge these are of major engineering importance because failure theories directly or indirectly involve them in isotropic materials one may compute analytically the eigen functions and their shadows z yosibash n omer m costabel m dauge edge stress intensity functions in polyhedral domains and their extraction by a quasi dual function method int j fract 136 2005 37 73 used in conjunction with the quasi dual function method m costabel m dauge z yosibash a quasi dual function method for extracting edge stress intensity functions siam j math anal 35 5 2004 1177 1202 for extracting esifs from finite element solutions however in anisotropic materials and multi material interfaces the analytical derivation becomes intractable and numerical methods are mandatory herein we use p finite element methods p fem for the computation of the eigen pairs and shadow functions together with their duals having computed these the p fem is used again to obtain a fe solution from which we extract approximations of the esifs based on a family of adaptive hierarchical jacobi polynomials of increasing order numerical examples for 3 d isotropic and anisotropic materials are provided for which the eigen pairs and shadow functions are numerically computed and esifs extracted these examples show the efficiency and high accuracy of the numerical approximations 2007 elsevier b v all rights reserved

weighted regularization of maxwell equations in polyhedral domains we present a new method of regularizing time harmonic maxwell equations by a bf grad div term adapted to the geometry of the domain this method applies to polygonal domains in two dimensions as well as to polyhedral domains in three dimensions in the presence of reentrant corners or edges the usual regularization is known to produce wrong solutions due the non density of smooth fields in the variational space we get rid of this undesirable effect by the introduction of special weights inside the divergence integral standard finite elements can then be used for the approximation of the solution this method proves to be numerically efficient

a numerical procedure for the determination of certain quantities related to the stress intensity factors in two dimensional elasticity abstract this work is devoted to the investigation of corner and interface singularities in linear elasticity and to the development of a numerical code that computes certain quantities associated with those singularities we compute several terms of the asymptotic expansion of the solution of the elasticity system near the corner or interface which is of the form knr nfn in particular the n and fn we treat our problem as a non linear eigenvalue problem and we use an approach based on the shooting method for boundary value problems to create an analytic function whose zeros are the n above the zeros of this function are then found using an iteration method and a global method to make sure that no zero was overlooked the program works for the general case of anisotropic non homogeneous wedge with general boundary conditions as well as in the case of crossing interfaces in an internal point we test the convergence accuracy robustness efficiency and reliability of the code from those tests it can be seen that the code works quite well for the majority of the applications

predictive value of statistical models a review is given of different ways of estimating the error rate of a prediction rule based on a statistical model a distinction is drawn between apparent optimum and actual error rates moreover it is shown how cross validation can be used to obtain an adjusted predictor with smaller error rate a detailed discussion is given for ordinary least squares logistic regression and cox regression in survival analysis finally the splitsample approach is discussed and demonstrated on two data sets

dirichlet to neumann map for domains with corners and approximate boundary conditions we present in this paper the dirichlet to neumann operator for the wave equation on a straight wedge in r 2 using fourier integral operators as a consequence we recover the classical approximate boundary conditions of orders 1 and 2

conditional parametric models for storm sewer runoff 1 the method of conditional parametric modeling is introduced for flow prediction in a sewage system it is a well known fact that in hydrological modeling the response runoff to input precipitation varies depending on soil moisture and several other factors consequently nonlinear input output models are needed the model formulation described in this paper is similar to the traditional linear models like final impulse response fir and autoregressive exogenous arx except that the parameters vary as a function of some external variables the parameter variation is modeled by local lines using kernels for local linear regression as such the method might be referred to as a nearest neighbor method the results achieved in this study were compared to results from the conventional linear methods fir and arx the increase in the coefficient of determination is substantial furthermore the new approach conserves the mass balance better hence this new approach looks promising for various hydrological models and analysis

an optimal selection of regression variables summary an asymptotically optimal selection of regression variables is proposed the key assumption is that the number of control variables is infinite or increases with the sample size it is also shown that mallows s qp akaike s fpe and aic methods are all asymptotically equivalent to this method

analysis of linear combinations with extreme ratios of variance abstract if the covariance matrices 1 and 2 of two multivariate populations are not identical insight into the differences between 1 and 2 can often be gained by analyzing the linear combinations with extreme ratios of variances that is those defined by the eigenvectors associated with the extreme roots of 1 1 2 this article gives a descriptive method similar to variable selection procedures in regression for screening and simplifying these linear combinations a hypothesis of redundancy of variables is defined and a statistic for testing this hypothesis is derived the method is illustrated by an example

preaveraged localized orthogonal polynomial estimators for surface smoothing and partial differentiation abstract we propose a multivariate smoothing method based on products of localized orthogonal polynomial series estimators for a smooth regression surface in the fixed design regression model the estimation of partial derivatives is included the proposed method provides for automatic and efficient boundary modifications near the edges of the surface assuming that the boundary of the support of the regression function satisfies some regularity conditions by allowing for a preaveraging step the corresponding algorithms are speeded up considerably and are easy to implement computation of special boundary kernels as required by the kernel method to avoid edge effects is not necessary it is shown that under sufficient smoothness assumptions the global average mean squared error has the same optimal rate of convergence as the mean squared error at an interior point that is the boundary correction is asymptotically effective the method depends on two smoothing parameters one determining the amount

semiparametric non linear time series model selection summary semiparametric time series regression is often used without checking its suitability resulting in an unnecessarily complicated model in practice one may encounter computational difficulties caused by the curse of dimensionality the paper suggests that to provide more precise predictions we need to choose the most significant regressors for both the parametric and the nonparametric time series components we develop a novel cross validation based model selection procedure for the simultaneous choice of both the parametric and the nonparametric time series components and we establish some asymptotic properties of the model selection procedure proposed in addition we demonstrate how to implement it by using both simulated and real examples our empirical studies show that the procedure works well

asymptotic optimality for c_p c_l cross validation and generalized cross validation discrete index set c p c l cross validation and generalized cross validation are useful data driven techniques for selecting a good estimate from a proposed class of linear estimates the asymptotic behaviors of these procedures are studied some easily interpretable conditions are derived to demonstrate the asymptotic optimality it is argued that cross validation and generalized cross validation can be viewed as some special ways of applying c l applications in nearest neighbor nonparametric regression and in model selection are discussed in detail

integrated square error properties of kernel estimators of regression functions weak laws of large numbers and central limit theorems are proyed for integrated square error of kernel estimators of regression functions the regressor is assumed to take values in rp and the regressand x to be real valued it is shown that in many cases integrated square error is asymptotically normally distributed and independent of the x sample as an application a test for the regression function such as that proposed by konakov is seen to be asymptotically independent of an arbitrary test based on the xsample the proofs involve martingale methods