large scale tikhonov regularization via reduction by orthogonal projection abstract this paper presents a new approach to computing an approximate solution of tikhonov regularized large scale ill posed least squares problems with a general regularization matrix the iterative method applies a sequence of projections onto generalized krylov subspaces a suitable value of the regularization parameter is determined by the discrepancy principle

on strong invariance principles under dependence assumptions on obtient des principes d invariance forts avec un ordre d approximation o t 1 2 k pour des suites de variables aleatoires dependantes

a new gradient regularization algorithm for source term inversion in 1d solute transportation with final observations abstract in this paper a new gradient regularization algorithm is introduced and applied to solve an inverse problem of determining source terms in one dimensional advection dispersion equation with final observations by functional approximations the algorithm is reduced to find an optimal perturbation for a given source parameter involving computations of gradient vectors in the case of using accurate data the optimal perturbation can be directly worked out by the least square method in the case of with random noisy data regularization strategy may be useful to the realization of the algorithm as compared with ordinary gradient regularization algorithm the new gradient regularization algorithm gives a possible approach to the precise choices of optimal regularization parameters several numerical simulations under different conditions are carried out showing that the algorithm is feasible and efficient furthermore the algorithm is successfully applied to solve a real life example of determining an average magnitude of groundwater pollution sources

on the balancing principle for some problems of numerical analysis we discuss a choice of weight in penalization methods the motivation for the use of penalization in computational mathematics is to improve the conditioning of the numerical solution one example of such improvement is a regularization where a penalization substitutes an ill posed problem for a well posed one in modern numerical methods for pdes a penalization is used for example to enforce a continuity of an approximate solution on non matching grids a choice of penalty weight should provide a balance between error components related with convergence and stability which are usually unknown in this paper we propose and analyze a simple adaptive strategy for the choice of penalty weight which does not rely on a priori estimates of above mentioned components it is shown that under natural assumptions the accuracy provided by our adaptive strategy is worse only by a constant factor than one could achieve in the case of known stability and convergence rates finally we successfully apply our strategy for self regularization of volterra type severely ill posed problems such as the sideways heat equation and for the choice of a weight in interior penalty discontinuous approximation on non matching grids numerical experiments on a series of model problems support theoretical results

regularization tools and robust optimization for ill conditioned least squares problem a computational comparison least squares problems arise frequently in many disciplines such as image restorations in these areas for the given least squares problem usually the coefficient matrix is ill conditioned thus if the problem data are available with certain error then after solving least squares problem with classical approaches we might end up with a meaningless solution tikhonov regularization is one of the most widely used approaches to deal with such situations in this paper first we briefly describe these approaches then the robust optimization framework which includes the errors in problem data is presented finally our computational experiments on several ill conditioned standard test problems using the regularization tools a matlab package for least squares problem and the robust optimization framework show that the latter approach may be the right choice

strassen type functional laws for strong topologies letw denote a wiener process the functional law of the iterated logarithm due to strassen 1964 establishes that the sequence 2nlln 1 2w ns of functions ofs 0 1 is almost surely compact in the uniform topology and gives a simple description of the corresponding limit set in this paper we obtain a general characterization of the topologies under which this statement remains valid

determining surface temperatures from interior observations we consider the inverse heat transfer problem for the case of the one dimensional heat equation in a quarter plane and present a new solution algorithm together with error bounds of logarithmic convexity type our method is based on regularizing the initial value problem for the heat equation run sideways we describe a numerical experiment with rapidly varying temperature profiles and explain how the method can be extended to problems with temperature dependent thermal properties

generalized arnoldi tikhonov method for sparse reconstruction this paper introduces two new algorithms belonging to the class of arnoldi tikhonov regularization methods which are particularly appropriate for sparse reconstruction the main idea is to consider suitable adaptively defined regularization matrices that allow the usual 2 norm regularization term to approximate a more general regularization term expressed in the p norm p geq 1 the regularization matrix can be updated both at each step and after some iterations have been performed leading to two different approaches the first one is based on the idea of the iteratively reweighted least squares method and can be obtained considering flexible krylov subspaces the second one is based on restarting the arnoldi algorithm numerical examples are given in order to show the effectiveness of these new methods and comparisons with some other already existing algorithms are made

a vector valued almost sure invariance principle for hyperbolic dynamical systems we prove an almost sure invariance principle approximation by d dimensional brownian motion for vector valued holder observables of large classes of nonuniformly hyperbolic dynamical systems these systems include axiom a dieomorphisms and flows as well as systems modelled by young towers with moderate tail decay rates in particular the position variable of the planar periodic lorentz gas with finite horizon approximates a 2 dimensional brownian motion

a discontinuous hp finite element method for diffusion problems 1 d analysis abstract this paper presents the mathematical analysis of a new variant of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems not requiring auxiliary variables such as those used in mixed methods the focus of this study is on a class of linear second order boundary value problems for which we prove stability and a priori error estimates in both the finite and infinite dimensional spaces

some applications of isoperimetric methods to strong limit theorems for sums of independent random variables we develop several applications to almost sure limit theorems for sums of independent vector valued random variables of an isoperimetric inequality due to talagrand a general treatment of the classical laws of large numbers of kolmogorov and prokorov and laws of the iterated logarithm of kolmogorov and hartman and wintner is described new results as well as simpler new proofs of known ones illustrate the usefulness of isoperimetric methods in this context we show further how this approach can be used in the study of limit theorems for trimmed sums of independent and identically distributed random variables 1 introduction and theoretical statement isoperimetric methods already appeared in the study of strong limit theorems for sums of independent vector valued random variables through concentration inequalities mainly of gaussian type these inequalities are commonly used with the tool of randomization and applied conditionally in particular this was the basic idea of the main result of 24 which characterizes banach space valued random variables satisfying the classical hartman wintner strassen law of the iterated logarithm in a recent work 32 a new isoperimetric inequality for product measures was obtained and applied to the integrability of sums of independent vector valued random variables providing at the same time new perspectives in the study of strong limit theorems this inequality was indeed further applied in 25 to get extensions of kolmogorov s law of the iterated logarithm and prokorov s law of large numbers in banach space the purpose of this article is to demonstrate further the usefulness of this approach we study a general statement section 2 on sums of independent banach space valued random

strong invariance principles for mixing random fields given a random field z q indexed by q tuples of positive integers and satisfying a strong mixing condition we study the approximation of the partial sum field sn n z q by brownian sheet setting g alpha n 1 n q in z q n k underset raise0 3em hbox smash scriptscriptstyle geqslant mathop pi limits 1 underset raise0 3em hbox smash scriptscriptstyle leqslant i underset raise0 3em hbox smash scriptscriptstyle leqslant q i pm k n i alpha k 1 q for 0 0 we also construct an example showing that in a somewhat larger similar type domain the above approximation is generally impossible even with 0

characterization of lil behavior in banach space in a recent paper by the authors a general result characterizing two sided lil behavior for real valued random variables has been established in this paper we look at the corresponding problem in the banach space setting we show that there are analogous results in this more general setting in particularly we provide a necessary and sufficient condition for lil behavior with respect to sequences of the form p nh n where h is from a suitable subclass of the positive nondecreasing slowly varying functions to prove these results we have to use a different method one of our main tools is an improved fuk nagaev type inequality in banach space which should be of independent interest

asymptotic inference for dynamic panel estimators of infinite order autoregressive processes abstract in this paper we consider the estimation of a dynamic panel autoregressive ar process of possibly infinite order in the presence of individual effects we employ double asymptotics under which both the cross sectional sample size and the length of time series tend to infinity and utilize the sieve ar approximation with its lag order increasing with the sample size we establish the consistency and asymptotic normality of the fixed effects estimator and propose a bias corrected fixed effects estimator based on a theoretical asymptotic bias term monte carlo simulations demonstrate the usefulness of bias correction as an illustration the proposed methods are applied to dynamic panel estimation of the law of one price deviations among us cities

on a preference based instrumental variable approach in reducing unmeasured confounding by indication treatment preferences of groups e g clinical centers have often been proposed as instruments to control for unmeasured confounding by indication in instrumental variable iv analyses however formal evaluations of these group preference based instruments are lacking unique challenges include the following i correlations between outcomes within groups ii the multi value nature of the instruments iii unmeasured confounding occurring between and within groups we introduce the framework of between group and within group confounding to assess assumptions required for the group preference based iv analyses our work illustrates that when unmeasured confounding effects exist only within groups but not between groups preference based ivs can satisfy assumptions required for valid instruments we then derive a closed form expression of asymptotic bias of the two stage generalized ordinary least squares estimator when the ivs are valid simulations demonstrate that the asymptotic bias formula approximates bias in finite samples quite well particularly when the number of groups is moderate to large the bias formula shows that when the cluster size is finite the iv estimator is asymptotically biased only when both the number of groups and cluster size go to infinity the bias disappears however the iv estimator remains advantageous in reducing bias from confounding by indication the bias assessment provides practical guidance for preference based iv analyses to increase their performance one should adjust for as many measured confounders as possible consider groups that have the most random variation in treatment assignment and increase cluster size to minimize the likelihood for these ivs to be invalid one should minimize unmeasured between group confounding copyright 2014 john wiley sons ltd

preconditioner based on the sherman morrison formula for regularized least squares problems we propose a sparse approximate inverse preconditioner based on the sherman morrison formula for tikhonov regularized least square problems theoretical analysis shows that the factorization method can take the advantage of the symmetric property of the coefficient matrix and be implemented cheaply combined with dropping rules the incomplete factorization leads to a preconditioner for krylov iterative methods to solve regularized least squares problems numerical experiments show that our preconditioner is competitive compared to existing methods especially for ill conditioned and rank deficient least squares problems

asymptotically unbiased inference for a dynamic panel model with fixed effects when both n and t are large we consider a dynamic panel ar 1 model with fixed effects when both n and t are large under the t fixed n large asymptotic approximation the ordinary least squares ols or gaussian maximum likelihood estimator mle is known to be inconsistent due to the well known incidental parameter problem we consider an alternative asymptotic approximation where n and t grow at the same rate it is shown that although ols or the mle is asymptotically biased a relatively simple fix to ols or the mle results in an asymptotically unbiased estimator under the assumption of gaussian innovations the bias corrected mle is shown to be asymptotically efficient by a hajek type convolution theorem

a new regularization method for the time fractional inverse advection dispersion problem in this paper we consider the time fractional inverse advection dispersion problem tfiadp in a quarter plane the solute concentration and dispersion flux are sought from a measured concentration history at a fixed location inside the body such a problem is obtained from the classical advection dispersion equation by replacing the first order time derivative with the caputo fractional derivative of order alpha 0 alpha 1 we show that the tfiadp is severely ill posed and we further apply a new regularization method to solve it based on the solution given by the fourier method convergence estimates are presented under a priori bound assumptions for the exact solution finally one numerical example is given to show that the proposed numerical method is effective

optimal stability for the inverse problemof multiple cavities abstract we deal with the determination of finitely many cavities in a planar inhomogeneous conductor from one current and voltage measurement collected on the exterior boundary we prove stability estimates under essentially minimal a priori regularity assumptions we construct an explicit example showing the optimality of such stability estimates

the time series and cross section asymptotics of dynamic panel data estimators in this paper we derive the asymptotic properties of within groups wg gmm and liml estimators for an autoregressive model with random effects when both t and n tend to infinity gmm and liml are consistent and asymptotically equivalent to the wg estimator when t n 0 the fixed t results for gmm and liml remain valid but wg although consistent has an asymptotic bias in its asymptotic distribution when t n tends to a positive constant the wg gmm and liml estimators exhibit negative asymptotic biases of order 1 t 1 n and 1 2n t respectively in addition the crude gmm estimator that neglects the autocorrelation in first differenced errors is inconsistent as t n c 0 despite being consistent for fixed t finally we discuss the properties of a random effects pseudo mle with unrestricted initial conditions when both t and n tend to infinity

lavrentiev regularization ritz approximation uniform finite element error estimates for differential equations with rough coefficients we consider a parametric family of boundary value problems for a diffusion equation with a diffusion coefficient equal to a small constant in a subdomain such problems are not uniformly well posed when the constant gets small however in a series of papers bakhvalov and knyazev have suggested a natural splitting of the problem into two well posed problems using this idea we prove a uniform finite element error estimate for our model problem in the standard parameter independent sobolev norm we also study uniform regularity of the transmission problem needed for approximation a traditional finite element method with only one additional assumption namely that the boundary of the subdomain with the small coefficient does not cut any finite element is considered one interpretation of our main theorem is in terms of regularization our fem problem can be viewed as resulting from a lavrentiev regularization and a ritz galerkin approximation of a symmetric ill posed problem our error estimate can then be used to find an optimal regularization parameter together with the optimal dimension of the approximation subspace

discretized tikhonov regularization for robin boundaries localization we deal with a boundary detection problem arising in nondestructive testing of materials the problem consists in recovering an unknown portion of the boundary where a robin condition is satisfied with the use of a cauchy data pair collected on the accessible part of the boundary we combine a linearization argument with a tikhonov regularization approach for the local reconstruction of the unknown defect moreover we discuss the regularization parameter choice by means of the so called balancing principle and we present some numerical tests that show the efficiency of our method

self regularization by projection for noisy pseudodifferential equations of negative order it is well known that pseudodifferential equations of negative order considered in sobolev spaces with small smoothness indices are ill posed on the other hand it is known that efficient discretization schemes with properly chosen discretization parameters allow to obtain a regularization effect for such equations the main accomplishment of the present paper is the principle for the adaptive choice of the discretization parameters directly from noisy discrete data we argue that the combination of this principle with wavelet based matrix compression techniques leads to algorithms which are order optimal in the sense of complexity

limit theorems for sums of weakly dependent banach space valued random variables we prove an estimate for the prohorov distance in the central limit theorem for strong mixing banach space valued random variables using a recent variant of an approximation theorem of berkes and philipp 1979 we obtain as a corollary a strong invariance principle for absolutely regular sequences with error term t tfrac 1 2 gamma for strong mixing sequences we prove a strong invariance principle with error term o t log logt 1 2

an almost sure invariance principle for hilbert space valued martingales we obtain an almost sure approximation of a martingale with values in a real separable hilbert space h by a suitable h valued brownian motion

application of the ritz galerkin method for recovering the spacewise coefficients in the wave equation an inverse problem for the determination of the unknown spacewise dependent coefficients in a hyperbolic equation through additional boundary measurements is considered for the sake of simplicity the problem has been considered in one dimension however the method is applicable for problems with regular and bounded domains in higher dimensions the technique provides space time approximations for the wave equation by expanding the required approximate solutions using the bernstein multi scaling functions the key feature of the approach is applying the ritz galerkin method along with utilizing the satisfier function which fulfills all the initial and boundary conditions as well as the consequences only a low number of basis is required to find satisfactory results which lead to reliably less computations in comparison to other published methods despite the assumptions of sufficiently smooth initial and boundary conditions to guarantee a unique solution this solution is unstable this fact is confirmed by the numerical findings that show the errors in the approximations are relatively large i e they are not of the same order compared to the noise levels greater than 3 hence the problem is ill posed to alleviate the difficulties arising from solving the ill posed problems a type of particular regularization technique which consists in repeatedly linearizing the operator equation f x y is utilized numerical results are presented for the typical benchmark test examples which have the input measured data perturbed by increasing amounts of noise the numerical investigations are included showing that accurate and stable results can be obtained efficiently with small computational cost

the central limit theorem for empirical processes under local conditions the case of radon infinitely divisible limits without gaussian component on obtient des resultats de convergence faible pour des processus empiriques indices par des classes f de fonctions dans le cas de limites de radon purement de poisson infiniment divisibles

pointwise error estimates of the local discontinuous galerkin method for a second order elliptic problem in this paper we derive some pointwise error estimates for the local discontinuous galerkin ldg method for solving second order elliptic problems in r n n 2 our results show that the pointwise errors of both the vector and scalar approximations of the ldg method are of the same order as those obtained in the l 2 norm except for a logarithmic factor when the piecewise linear functions are used in the finite element spaces moreover due to the weighted norms in the bounds these pointwise error estimates indicate that when at least piecewise quadratic polynomials are used in the finite element spaces the errors at any point z depend very weakly on the true solution and its derivatives in the regions far away from z these localized error estimates are similar to those obtained for the standard conforming finite element method

bias in dynamic panel models under time series misspecification abstract we consider within group estimation of higher order autoregressive panel models with exogenous regressors and fixed effects where the lag order is possibly misspecified even when disregarding the misspecification bias the fixed effect bias formula is quite different from the correctly specified case though its asymptotic order remains the same under the stationarity we suggest bias reduction methods under the possible time series misspecification

bootstrapping general empirical measures it is proved that the bootstrapped central limit theorem for empirical processes indexed by a class of functions mathscr f and based on a probability measure p holds a s if and only if mathscr f in mathrm clt p and int f 2 dp infty where f sup f in mathscr f f and it holds in probability if and only if mathscr f in mathrm clt p thus for a large class of statistics no local uniformity of the clt about p is needed for the bootstrap to work consistency of the bootstrap the bootstrapped law of large numbers is also characterized these results are proved under certain weak measurability assumptions on mathscr f

effects of not knowing the order of an autoregressive process on the mean squared error of prediction i abstract given a realization of t consecutive observations of an autoregressive process x of unknown order m a process of an arbitrary order p is assumed to be fitted for predicting the future values of another process xtilde t where xtilde t is independent of xt but otherwise has identical probabilistic structure the mean squared error of prediction when the autoregressive coefficients are estimated by least squares is obtained to terms of order t 1 the bias in estimating the autoregressive coefficients is examined the results are illustrated for three processes with m 2 by considering fitting of a process with p 1

the role of the penalty in the local discontinuous galerkin method for maxwell s eigenvalue problem abstract the local discontinuous galerkin ldg method is a promising emerging technology for discretizing a wide range of differential operators it is well known that the robustness of this method is contingent upon a stabilization term we analyze the role of this term in the ldg discretization of the maxwell curl curl operator demonstrating that the stabilization parameter can be used to split the spectrum into two sections the first set of eigenvalues approximate the spectrum of the curl conforming finite element curl curl operator while the second set are spurious eigenvalues that can be made arbitrarily large by increasing the stabilization parameter we confirm this analysis with a range of computational experiments that compare the spectra obtained from ldg and curl conforming discretizations

on the law of the iterated logarithm for independent banach space valued random variables in this paper we establish some general forms of the law of the iterated logarithm for independent random variables xn with banach space values where xn is not necessarily identically distributed our results include the kolmogorov law of the iterated logarithm lil in both finite and infinite dimensional cases and they improve the wittmann lil as well as extend it to the vector setting the ledoux talagrand lil for an i i d sequence is also a simple corollary of our results

characterization of the law of the iterated logarithm in banach spaces on utilise une technique de randomisation gaussienne pour demontrer qu une variable aleatoire a valeurs dans un espace de banach satisfait la loi du logarithme itere sous une certaine condition necessaire et suffisante

a modified tikhonov regularization method tikhonov regularization and truncated singular value decomposition tsvd are two elementary techniques for solving a least squares problem from a linear discrete ill posed problem based on these two techniques a modified regularization method is proposed which is applied to an arnoldi based hybrid method theoretical analysis and numerical examples are presented to illustrate the effectiveness of the method

properties of predictors in misspecified autoregressive time series models abstract this article investigates major effects of misspecification in stationary linear time series models when we fit a pth order autoregressive model the true model can be an autoregressive moving average model we derive the formulas of bias and mean squared error mse of the least squares estimator and the hth period ahead prediction mse in the time domain contrary to previous studies the process in estimation is not necessarily independent of the process in prediction and the distribution of process is not necessarily gaussian we examine the effects of this dependence and nonnormality on prediction in misspecified models

almost optimal interior penalty discontinuous approximations of symmetric elliptic problems on non matching grids we consider an interior penalty discontinuous approximation for symmetric elliptic problems of second order on non matching grids in this paper the main result is an almost optimal error estimate for the interior penalty approximation of the original problem based on partitioning of the domain into a finite number of subdomains further an error analysis for the finite element approximation of the penalty formulation is given finally numerical experiments on a series of model second order problems are presented

logarithmic convergence rates for the identification of a nonlinear robin coefficient we consider the identification of a nonlinear corrosion profile from single voltage boundary data and show injectivity of the parameter to output map we demonstrate that tikhonov regularization can be applied in order to solve the inverse problem in a stable manner despite the presence of noisy data in combination with a logarithmic stability estimate for the underlying cauchy problem rates for the convergence of the regularized solutions are proven using a source condition that does not involve the frechet derivative of the parameter to output map we present sufficient conditions for the existence of a source function and illustrate our approach by means of numerical examples

some results on the lil in banach space with applications to weighted empirical processes we examine the cluster set of s n a n for banach space valued random variables and investigate the relationship between the central limit theorem and the law of the iterated logarithm in this setting in the case of hilbert space valued random variables necessary and sufficient conditions are given for the law of the iterated logarithm some interesting examples are also included we then apply our results to weighted empiricals both in the supremum norm and the l 2 lbrack 0 1 rbrack norm

bias in dynamic panel estimation with fixed effects incidental trends and cross section dependence abstract explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size n the results extend earlier work by nickell 1981 biases in dynamic models with fixed effects econometrica 49 1417 1426 and later authors in several directions that are relevant for practical work including models with unit roots deterministic trends predetermined and exogenous regressors and errors that may be cross sectionally dependent the asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coefficient another finding of interest is that when there is cross section error dependence the probability limit of the dynamic panel regression estimator is a random variable rather than a constant which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where n is very large some proposals for bias correction are suggested and finite sample performance is analyzed in simulations

adaptive estimation of linear functionals in hilbert scales from indirect white noise observations we consider adaptive estimating the value of a linear functional from indirect white noise observations for a flexible approach the problem is embedded in an abstract hilbert scale we develop an adaptive estimator that is rate optimal within a logarithmic factor simultaneously over a wide collection of balls in the hilbert scale it is shown that the proposed estimator has the best possible adaptive properties for a wide range of linear functionals the case of discretized indirect white noise observations is studied and the adaptive estimator in this setting is developed

linearization of a free boundary problem in corrosion detection abstract we consider a boundary identification problem arising in nondestructive testing of materials the problem is to recover a part i of the boundary of a bounded planar domain from one cauchy data pair u u of a harmonic potential u in collected on an accessible boundary subset a we prove frechet differentiability of a suitably defined forward map and discuss local uniqueness and lipschitz stability results for the linearized problem

bootstrap inference for linear dynamic panel data models with individual fixed effects abstract this paper s main contribution is to propose and theoretically justify the application of bootstrap methods for inference in autoregressive panel data models with fixed effects whereas the focus of the existing literature has been on bias correcting the standard fixed effects ols estimator due to the well known incidental parameter bias our focus here is on improving the quality of inference by relying on the bootstrap instead of the standard normal distribution when computing critical values for test statistics in particular we show by simulation that confidence intervals based on the normal distribution can be very distorted in finite samples instead a bootstrap that resamples the residuals and generates the bootstrap observations recursively using the estimated autoregressive panel data model greatly reduces these distortions we show that this recursive design residual based bootstrap fixed effects ols estimator contains a built in bias correction term that mimics the incidental parameter bias thus this method can be used to approximate the bias as well as the entire distribution of the biased fixed effects ols estimator this is in contrast with two other methods we consider a fixed design residual based bootstrap and a pairs bootstrap whose distributions are incorrectly centered at zero as it turns out both the recursive design and the pairs bootstrap are asymptotically valid when applied to the bias corrected estimator but the fixed design bootstrap is not in the simulations the recursive design bootstrap is the method that does best overall

un critere sur les petites boules dans le theoreme limite central we show that a banach space valued random variablex such that mathop lim limits x to infty t 2 mathbb p left left x right t right 0 satisfies the central limit theorem if and only if the following criterion on small balls is fulfilled mathop lim limits x to infty t 2 mathbb p left left x right t right 0

a variant of tikhonov regularization for parabolic pde with space derivative multiplied by a small parameter in this paper we examine the applicability of a variant of tikhonov regularization for parabolic pde with its highest order space derivative multiplied by a small parameter the solution of the operator equation u t 2 u x 2 a x t f x t is not uniformly convergent to the solution of the operator equation u t a x t f x t when 0 this violates one of the conditions of hadamard well posedness and hence the perturbed parabolic operator equation is ill posed since the operator is unbounded we first discuss the general theory for unbounded operators and propose an a posteriori parameter choice rule for choosing a regularization parameter we then apply these techniques in the context of perturbed parabolic problems finally we implement our regularized scheme and compare with other basic existing schemes to assert the adaptability of the scheme as an alternate approach for solving the problem

model selection in the presence of incidental parameters this paper considers model selection in panels where incidental parameters are present primary interest centers on selecting a model that best approximates the underlying structure involving parameters that are common within the panel it is well known that conventional model selection procedures are often inconsistent in panel models and this can be so even without nuisance parameters modifications are then needed to achieve consistency new model selection information criteria are developed here that use either the kullback leibler information criterion based on the profile likelihood or the bayes factor based on the integrated likelihood with a bias reducing prior these model selection criteria impose heavier penalties than those associated with standard information criteria such as aic and bic the additional penalty which is data dependent properly reflects the model complexity arising from the presence of incidental parameters a particular example is studied in detail involving lag order selection in dynamic panel models with fixed effects the new criteria are shown to control for over under selection probabilities in these models and lead to consistent order selection criteria

almost sure behaviour of f valued random fields letx n n d be a field of independent random variables taking values in a semi normed measurable vector spacef for a broad class of fields n d of positive numbers the almost sure behaviour of k nxk n n d is studied the main result allows us to deduce some new and well known theorems for fields of independentf random variables from related results for fields of independent real random variables

linear regression limit theory for nonstationary panel data this paper develops a regression limit theory for nonstationary panel data with large numbers of cross section n and time series t observations the limit theory allows for both sequential limits wherein t followed by n and joint limits where t n simultaneously and the relationship between these multidimensional limits is explored the panel structures considered allow for no time series cointegration heterogeneous cointegration homogeneous cointegration and near homogeneous cointegration the paper explores the existence of long run average relations between integrated panel vectors when there is no individual time series cointegration and when there is heterogeneous cointegration these relations are parameterized in terms of the matrix regression coefficient of the long run average covariance matrix in the case of homogeneous and near homogeneous cointegrating panels a panel fully modified regression estimator is developed and studied the limit theory enables us to test hypotheses about the long run average parameters both within and between subgroups of the full population

analysis of finite element domain embedding methods for curved domains using uniform grids we analyze the error of a finite element domain embedding method for elliptic equations on a domain omega with curved boundary the domain is embedded in a rectangle r on which uniform mesh and linear continuous elements are employed the numerical scheme is based on an extension of the differential equation from omega to r by regularization with a small parameter epsilon for neumann and robin problems or penalty with a large parameter epsilon 1 for the dirichlet problem or a mixture of these for a mixed boundary value problem for neumann and robin problems we prove that when epsilon le h the mesh size the error in the h 1 omega norm is of the optimal order mathcal o h for the dirichlet problem when epsilon le h 1 2 the error is mathcal o h 1 2 that is not optimal if the mesh is adjusted around partial omega to fit it then the optimal convergence rate mathcal o h holds for the dirichlet problem if omega is convex and epsilon le h if omega is not convex then the convergence rate can only be improved to mathcal o h 2 3 by such mesh adjustment with the parameter being epsilon h 2 3 in this latter case a parameter smaller than h 2 3 thwarts the convergence rate which is verified by a numerical result

an almost sure invariance principle for stationary ergodic sequences of banach space valued random variables in this paper we establish an almost sure invariance principle with an error termo t log logt 1 2 ast for partial sums of stationary ergodic martingale difference sequences taking values in a real separable banach space as partial sums of weakly dependent random variables can often be well approximated by martingales this result also leads to almost sure invariance principles for a wide class of stationary ergodic sequences such as o mixing and mixing sequences and functionals of such sequences compared with previous related work for vector valued random variables starting with an article by kuelbs and philipp 27 the present approach leads to a unification of the theory at least for stationary sequences moment conditions required by earlier authors are relaxed only second order weak moments are needed and our proofs are easier in that we do not employ estimates of the rate of convergence in the central limit theorem but merely the central limit theorem itself

on the adaptive selection of the parameter in regularization of ill posed problems we study the possibility of using the structure of the regularization error for a posteriori choice of the regularization parameter as a result a rather general form of a selection criterion is proposed and its relation to the heuristical quasi optimality principle of tikhonov and glasko z vychisl mat mat fiz 4 1964 pp 564 571 and to an adaptation scheme proposed in a statistical context by lepskii theory probab appl 36 1990 pp 454 466 is discussed the advantages of the proposed criterion are illustrated by using such examples as self regularization of the trapezoidal rule for noisy abel type integral equations lavrentiev regularization for nonlinear ill posed problems and an inverse problem of the two dimensional profile reconstruction

a tikhonov regularized penalty function approach for solving polylinear programming problems abstract this paper suggests a new regularized penalty method for poly linear functions until our knowledge it is the first time that a regularization approach solution for poly linear programming is reported in the literature we propose a penalty function depending on two parameters and for ensuring the strong convexity and the existence of a unique solution involving equality and inequality constraints we prove that if the penalty parameter tends to zero then the solution of the original problem converges to a unique solution with the minimal weighted norm we introduce a recurrent procedure based on the projection gradient method for finding the extremal points and we also prove the convergence of the method we develop an example for game theory and additional example for portfolio optimization employing the proposed regularization method for markov chains involving the definition of a poly linear function

on rates of convergence for sample average approximations in the almost sure sense and in mean we study the rates at which optimal estimators in the sample average approximation approach converge to their deterministic counterparts in the almost sure sense and in mean to be able to quantify these rates we consider the law of the iterated logarithm in a banach space setting and first establish under relatively mild assumptions almost sure convergence rates for the approximating objective functions which can then be transferred to the estimators for optimal values and solutions of the approximated problem by exploiting a characterisation of the law of the iterated logarithm in banach spaces we are further able to derive under the same assumptions that the estimators also converge in mean at a rate which essentially coincides with the one in the almost sure sense this in turn allows to quantify the asymptotic bias of optimal estimators as well as to draw conclusive insights on their mean squared error and on the estimators for the optimality gap finally we address the notion of convergence in probability to derive rates in probability for the deviation of optimal estimators and weak rates of error probabilities without imposing strong conditions on exponential moments we discuss the possibility to construct confidence sets for the optimal values and solutions from our obtained results and provide a numerical illustration of the most relevant findings

a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

future sequential regularization methods for iii posed volterra equations applications to the inverse heat conduction problem abstract we develop a theoretical context in which to study the future sequential regularization method developed by beck for the inverse heat conduction problem in the process we generalize beck s ideas and view that method as one in a large class of regularization methods in which the solution of an ill posed first kind volterra equation is seen to be the limit of a sequence of solutions of well posed second kind volterra equations such techniques are important because standard regularization methods such as tikhonov regularization tend to transform a naturally sequential volterra problem into a full domain fredholm problem destroying the underlying causal nature of the volterra model and leading to inefficient global approximation strategies in contrast the ideas we present here preserve the original volterra structure of the problem and thus can lead to easily implemented localized approximation strategies theoretical properties of these methods are discussed and proofs of convergence are given

identification of a temperature dependent heat conductivity from single boundary measurements considering the identification of a temperature dependent conductivity in a quasilinear elliptic heat equation from single boundary measurements we proof uniqueness in dimensions n ge 2 taking noisy data into account we apply tikhonov regularization in order to overcome the instabilities by using a problem adapted adjoint we give convergence rates under substantially weaker and more realistic conditions than required by the general theory our theory is supported by numerical tests

implementations of range restricted iterative methods for linear discrete ill posed problems abstract this paper is concerned with iterative solution methods for large linear systems of equations with a matrix of ill determined rank and an error contaminated right hand side the numerical solution is delicate because the matrix is very ill conditioned and may be singular it is natural to require that the computed iterates live in the range of the matrix when the latter is symmetric because then the iterates are orthogonal to the null space computational experience indicates that it can be beneficial to require that the iterates live in the range of the matrix also when the latter is nonsymmetric we discuss the design and implementation of iterative methods that determine iterates with this property new implementations that are particularly well suited for use with the discrepancy principle are described

on bias inconsistency and efficiency of various estimators in dynamic panel data models abstract when a model for panel data includes lagged dependent explanatory variables then the habitual estimation procedures are asymptotically valid only when the number of observations in the time dimension t gets large usually however such datasets have substantial sample size in the cross section dimension n whereas t is often a single digit number results on the asymptotic bias n in this situation have been published a decade ago but hence far analytic small sample assessments of the actual bias have not been presented here we derive a formula for the bias of the least squares dummy variable lsdv estimator which has a o n 1 t 3 2 approximation error in a simulation study this is found to be remarkably accurate due to the small variance of the lsdv estimator which is usually much smaller than the variance of consistent generalized method of moments estimators a very efficient procedure results when we remove the bias from the lsdv estimator the simulations contain results for a particular operational corrected lsdv estimation procedure which in many situations proves to be much more efficient than various instrumental variable type estimators

convergence analysis of tikhonov type regularization algorithms for multiobjective optimization problems in this paper we introduce a vector valued tikhonov type regularization algorithm for an extended valued multiobjective optimization problem under some mild conditions we prove that any sequence generated by this algorithm converges to a weak pareto optimal solution of the multiobjective optimization problem our results improve and generalize some known results

invariance principles for sums of banach space valued random elements and empirical processes almost sure and probability invariance principles are established for sums of independent not necessarily measurable random elements with values in a not necessarily separable banach space it is then shown that empirical processes readily fit into this general framework thus we bypass the problems of measurability and topology characteristic for the previous theory of weak convergence of empirical processes