efficient estimates in semiparametric additive regression models with unknown error distribution several authors have shown how to efficiently estimate beta in the semiparametric additive model y x beta g t text error g t smooth but unknown when the error distribution is normal however the general theory suggests that efficient estimation should be possible for general error distributions with finite fisher information even when the error distribution is unknown in this note we construct a sequence of estimators which achieves this goal under technical assumptions

a posteriori error estimation for an augmented mixed primal method applied to sedimentation consolidation systems abstract in this paper we develop the a posteriori error analysis of an augmented mixed primal finite element method for the 2d and 3d versions of a stationary flow and transport coupled system typically encountered in sedimentation consolidation processes the governing equations consist in the brinkman problem with concentration dependent viscosity written in terms of cauchy pseudo stresses and bulk velocity of the mixture coupled with a nonlinear advection nonlinear diffusion equation describing the transport of the solids volume fraction we derive two efficient and reliable residual based a posteriori error estimators for a finite element scheme using raviart thomas spaces of order k for the stress approximation and continuous piecewise polynomials of degree k 1 for both velocity and concentration for the first estimator we make use of suitable ellipticity and inf sup conditions together with a helmholtz decomposition and the local approximation properties of the clement interpolant and raviart thomas operator to show its reliability whereas the efficiency follows from inverse inequalities and localisation arguments based on triangle bubble and edge bubble functions next we analyse an alternative error estimator whose reliability can be proved without resorting to helmholtz decompositions finally we provide some numerical results confirming the reliability and efficiency of the estimators and illustrating the good performance of the associated adaptive algorithm for the augmented mixed primal finite element method

goal oriented adaptivity of mixed gmsfem for flows in heterogeneous media abstract we present an adaptive goal oriented framework with the mixed generalized multiscale finite element method gmsfem to numerically solve the flow problem in heterogeneous media in this paper three different error indicators are considered two goal oriented and one a standard adaptive method for the global error each is used to approximate a number of quantities of interest given by interior edge fluxes in a high contrast field following the setting of mixed gmsfem on each coarse neighborhood of the computational domain the local error indicator introduced here is computed by the product of the residual norms of the primal and dual variational equations over coarse neighborhoods numerical results demonstrate the efficiency of this goal oriented method in comparison to a multiscale implementation of the dual weighted residual method and a standard adaptive method

energy norm a posteriori error estimates for mixed finite element methods this paper deals with the a posteriori error analysis of mixed finite element methods for second order elliptic equations it is shown that a reliable and efficient error estimator can be constructed using a postprocessed solution of the method the analysis is performed in two different ways under a saturation assumption and using a helmholtz decomposition for vector fields

saddle point criteria for multi dimensional control optimisation problem involving first order pde constraints in this paper the multi dimensional control optimisation problem involving first order pde constraints is considered the absolute value penalty function method is used to solve the considered pro

efficient estimation of population level summaries in general semiparametric regression models this article considers a wide class of semiparametric regression models in which interest focuses on population level quantities that combine both the parametric and the nonparametric parts of the model special cases in this approach include generalized partially linear models generalized partially linear single index models structural measurement error models and many others for estimating the parametric part of the model efficiently profile likelihood kernel estimation methods are well established in the literature here our focus is on estimating general population level quantities that combine the parametric and nonparametric parts of the model e g population mean probabilities etc we place this problem in a general context provide a general kernel based methodology and derive the asymptotic distributions of estimates of these population level quantities showing that in many cases the estimates are semiparametric efficient for estimating the population mean with no missing data we s

a semiparametric maximum likelihood estimator this paper presents a procedure for analyzing a model in which the parameter vector has two parts a finite dimensional component 8 and a nonparametric component a the procedure does not require parametric modeling of but assumes that the true density of the data satisfies an index restriction the idea is to construct a parametric model passing through the true model and to estimate by setting the score for the parametric model to zero the score is estimated nonparametrically and the estimator is shown to be n consistent and asymptotically normal the estimator is then shown to attain the semiparametric efficiency bound characterized in begun et al 1983 for multivariate nonlinear regression simultaneous equations partially specified regression index regression censored regression switching regression and disequilibrium models in which the error densities are unknown

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

adaptive finite element approximation of multiphysics problems a fluid structure interaction model problem we consider computation of the displacement of an elastic object immersed into a viscous incompressible flow for simplicity we assume that the mechanics of the solid is governed by linear elastic

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

adaptive streamline diffusion finite element methods for stationary convection diffusion problems adaptive finite element methods for stationary convectiondiffusion problems are designed and analyzed the underlying discretization scheme is the shock capturing streamline diffusion method the adaptive algorithms proposed are based on a posteriori error estimates for this method leading to reliable methods in the sense that the desired error control is guaranteed a priori error estimates are used to show that the algorithms are efficient in a certain sense

goal oriented error estimation and adaptivity for fluid structure interaction using exact linearized adjoints we develop duality based a posteriori error estimates for functional outputs of solutions of steady fluid structure interaction problems the crucial complication in obtaining these estimates pertains to the derivation of the coupled dual exact linearized adjoint problem owing to the free boundary character of fluid structure interaction we present two approaches to derive the dual problem in the domain map linearization approach the fluid subproblem is first transformed to a fixed reference domain after which one essentially linearizes with respect to the domain transformation map in the shape linearization approach fluid unknowns are fixed in the current configuration and a very weak formulation of the fluid subproblem is then linearized using shape derivative techniques we show that the dual problems correspond to coupled fluid structure problems with nonstandard coupling conditions furthermore we present numerical experiments that demonstrate the consistency of the dual based error estimates and their usefulness in goal oriented adaptive mesh refinement

smooth optimum kernel estimators of densities regression curves and modes several criteria concerning the choice of kernels for the nonparametric estimation of functions and their derivatives are discussed a specific optimality criterion is described which applies to kernels of compact support and of different orders of smoothness the solutions of the corresponding variational problems are explicitly given many kernels discussed previously are obtained as special cases

semiparametric estimates of the relation between weather and electricity sales abstract a nonlinear relationship between electricity sales and temperature is estimated using a semiparametric regression procedure that easily allows linear transformations of the data this accommodates introduction of covariates timing adjustments due to the actual billing schedules and serial correlation the procedure is an extension of smoothing splines with the smoothness parameter estimated from minimization of the generalized cross validation criterion introduced by craven and wahba 1979 estimates are presented for residential sales for four electric utilities and are compared with models that represent the weather using only heating and cooling degree days or with piecewise linear splines

scalarization in vector optimization in this paper some scalar optimization problems are presented whose optimal solutions are also solutions of a general vector optimization problem this will be done for weakly minimal and minimal solutions respectively finally the results will be applied to a certain class of approximation problems

on single index coefficient regression models abstract in this article we investigate a class of single index coefficient regression models under dependence this includes many existing models such as the smooth transition threshold autoregressive star model of chan and tong the functional coefficient autoregressive far model of chen and tsay and the single index model of ichimura compared to the varying coefficient model of hastie and tibshirani our model can avoid the curse of dimensionality in multivariate nonparametric estimations another advantage of this model is that a threshold variable is chosen automatically an estimation method is proposed and the corresponding estimators are shown to be consistent and asymptotically normal some simulations and applications are also reported

asymptotic efficiency in estimation with conditional moment restrictions abstract in this paper bounds on asymptotic efficiency are derived for a class of non parametric models the data are independent and identically distributed according to some unknown distribution f there is a given function of the data and a parameter the restrictions are that a conditional expectation of this function is zero at some point in the parameter space this point is to be estimated if f is assumed to be a multinomial distribution with known finite support then the problem becomes parametric and the bound can be obtained from the information matrix this bound turns out to depend only upon certain conditional moments and not upon the support of the distribution since a general f can be approximated by a multinomial distribution the multinomial bound applies to the general case

exact penalty functions and stability in locally lipschitz programming in this paper we extend the theory of exact penalty functions for nonlinear programs whose objective functions and equality and inequality constraints are locally lipschitz arbitrary simple constraints are also allowed assuming a weak stability condition we show that for all sufficiently large penalty parameter values an isolated local minimum of the nonlinear program is also an isolated local minimum of the exact penalty function a tight lower bound on the parameter value is provided when certain first order sufficiency conditions are satisfied we apply these results to unify and extend some results for convex programming since several effective algorithms for solving nonlinear programs with differentiable functions rely on exact penalty functions our results provide a framework for extending these algorithms to problems with locally lipschitz functions

the asymptotic variance of semiparametric estimators this paper derives a general formula for the asymptotic variance of semiparametric estimators that accounts for the presence of nonparametric estimators of functions the general formula is specialized to show invariance of the asymptotic variance to the type of nonparametric estimator and to obtain correction terms for estimation of densities and mean square projections including conditional expectations regularity conditions for the validity of the formula are also given including primitive conditions for asymptotic normality when series estimators are present new examples considered include a semiparametric panel probit estimator and a series estimator of the average derivative copyright 1994 by the econometric society

goal oriented error estimation for fluid structure interaction problems in this work we present an adaptive finite element method for the numerical simulation of stationary fluid structure interaction problems the coupled system is given in a variational and monolithic arbitrary lagrangian eulerian framework we derive methods for goal oriented error estimation and mesh adaptation with the dual weighted residual method key to applying this error estimator is the underlying canonic variational formulation of the fluid structure interaction problem by mapping the flow problem to ale coordinates the developed method is applied to two and three dimensional stationary benchmark problems coupling the incompressible navier stokes equations with a nonlinear hyper elastic material law

exact penalty functions in constrained optimization in this paper formal definitions of exactness for penalty functions are introduced and sufficient conditions for a penalty function to be exact according to these definitions are stated thus providing a unified framework for the study of both nondifferentiable and continuously differentiable penalty functions in this framework the best known classes of exact penalty functions are analyzed and new results are established concerning the correspondence between the solutions of the constrained problem and the unconstrained minimizers of the penalty functions

an η approximation method in nonlinear vector optimization abstract in this paper a new approach for a solution of a nonlinear multiobjective programming problem is introduced an equivalent approximated vector optimization problem is constructed by a modification of the objective and the constraint functions in the original multiobjective programming problem the connection between weak efficient points in the original multiobjective programming problem and its equivalent approximated vector optimization problem is proved in this way optimality conditions for nonlinear constrained multiobjective programming problems having invex and or generalized invex objective and constraint functions with respect to the same functions are obtained

efficient estimation for semivarying coefficient models motivated by two practical problems we propose a new procedure for estimating a semivarying coefficient model asymptotic properties are established which show that the bias of the parameter estimator is of order h 3 when a symmetric kernel is used where h is the bandwidth and the variance is of order n 1 and efficient in the semiparametric sense undersmoothing is unnecessary for the root n consistency of the estimators therefore commonly used bandwidth selection methods can be employed a model selection method is also developed simulations demonstrate how the proposed method works some insights are obtained into the two motivating problems by using the proposed models

variance function partially linear single index models we consider heteroscedastic regression models where the mean function is a partially linear single index model and the variance function depends upon a generalized partially linear single index model we do not insist that the variance function depend only upon the mean function as happens in the classical generalized partially linear single index model we develop efficient and practical estimation methods for the variance function and for the mean function asymptotic theory for the parametric and nonparametric parts of the model is developed simulations illustrate the results an empirical example involving ozone levels is used to further illustrate the results and is shown to be a case where the variance function does not depend upon the mean function

analysis of field experiments by least squares smoothing summary assuming a smooth trend plus independent error model for the environmental effects in the yields of a field plot experiment least squares smoothing methods are developed to estimate both the treatment effects and the unknown trend treatment estimates are closely related to those resulting from a generalized least squares analysis in which the covariance structure for the environmental effects has a particular form however the main emphases are on the accuracy of treatment estimates under a fixed smooth trend plus error model and the exploratory power of the basic method to isolate trend effects of unknown form although the detailed development is for the one dimensional case generalizations of the smoothness concept and extensions to two dimensions are also discussed application of the basic method is illustrated on three data sets and the results compared with other analyses

the vector exact l1 penalty method for nondifferentiable convex multiobjective programming problems abstract in this paper the vector exact l 1 penalty function method for nondifferentiable convex multiobjective programming problems is analyzed the vector penalized optimization problem with the vector exact l 1 penalty function is defined conditions are given guaranteeing the equivalence of the sets of weak pareto optimal solutions of the considered nondifferentiable multiobjective programming problem and of the associated vector penealized optimization problem with the vector exact l 1 penalty function this equivalence is established for nondifferentiable vector optimization problems with convex functions

a new family of mixed finite elements in ir 3 we introduce two families of mixed finite element on conforming inh div and one conforming inh curl these finite elements can be used to approximate the stokes system

goal oriented a posteriori error estimation for the travel time functional in porous media flows in this article we consider the a posteriori error estimation and adaptive mesh refinement for the numerical approximation of the travel time functional arising in porous media flows the key application of this work is in the safety assessment of radioactive waste facilities in this setting the travel time functional measures the time taken for a nonsorbing radioactive solute transported by groundwater to travel from a potential site deep underground to the biosphere to ensure the computability of the travel time functional we employ a mixed formulation of darcy s law and conservation of mass together with raviart thomas h mathrm div omega conforming finite elements the proposed a posteriori error bound is derived based on a variant of the standard dual weighted residual approximation which takes into account the lack of smoothness of the underlying functional of interest the proposed adaptive refinement strategy is tested on both a simple academic test case and a problem based on the

energy norm a posteriori error estimation for discontinuous galerkin methods in this paper we present a residual based a posteriori error estimate of a natural mesh dependent energy norm of the error in a family of discontinuous galerkin approximations of elliptic problems the theory is developed for an elliptic model problem in two and three spatial dimensions and general nonconvex polygonal domains are allowed we also present some illustrating numerical examples

a local post processing technique for improving the accuracy in mixed finite element approximations a general simple post processing technique is given in this paper under certain conditions if an algorithm approximating a function u also provides a good approximation for its gradient and for some locally defined projection pu then by this method a better approximation for u can be easily obtained essentially the leading term of the error between u and its original approximation can be computed it is shown how the method may be applied to various mixed type finite element methods

efficient estimation and computation of parameters and nonparametric functions in generalized semi non parametric regression models abstract the efficiency of estimation for the parameters in semiparametric models has been widely studied in the literature bickel et al 1993 in this paper we study efficient estimators for both parameters and nonparametric functions in a class of generalized semi non parametric regression models which cover commonly used semiparametric models such as partially linear models partially linear single index models and two sample semiparametric models we propose a maximum likelihood principle combined with the local linear technique for estimating the parameters and nonparametric functions the proposed estimators of the parameters and a linear functional of the nonparametric functions are consistent and asymptotically normal and are further shown to be semiparametrically efficient an efficient computational algorithm to achieve the maximization is proposed extensive simulation experiments show the superiority of the proposed methods three real data examples are analyzed and presented as an illustration

kernel smoothing in partial linear models on considere deux methodes d estimation l une reliee aux splines de lissage partiels l autre motivee par une analyse de residus partielle

local asymptotics for regression splines and confidence regions in this paper we study the local behavior of regression splines in particular explicit expressions for the asymptotic pointwise bias and variance of regression splines are obtained in addition asymptotic normality for regression splines is established leading to the construction of approximate confidence intervals and confidence bands for the regression function

local partial likelihood estimation for lifetime data this paper considers a proportional hazards model which allows one to examine the extent to which covariates interact nonlinearly with an exposure variable for analysis of lifetime data a local partial likelihood technique is proposed to estimate nonlinear interactions asymptotic normality of the proposed estimator is established the baseline hazard function the bias and the variance of the local likelihood estimator are consistently estimated in addition a one step local partial likelihood estimator is presented to facilitate the computation of the proposed procedure and is demonstrated to be as efficient as the fully iterated local partial likelihood estimator furthermore a penalized local likelihood estimator is proposed to select important risk variables in the model numerical examples are used to illustrate the effectiveness of the proposed procedures

sufficiency of exact penalty minimization by employing a recently obtained error bound for differentiable convex inequalities it is shown that under appropriate constraint qualifications a minimum solution of an exact penalty function for a single value of the penalty parameter which exceeds a certain threshold is also a solution of the convex program associated with the penalty function no a priori assumption is made regarding the solvability of the convex program if such a solvability assumption is made then we show that a threshold value of the penalty parameter can be used which is smaller than both the above mentioned value and that of zangwill these various threshold values of the penalty parameter also apply to the well known big m method of linear programming

goal oriented adaptivity for coupled flow and transport problems with applications in oil reservoir simulations goal oriented adaptivity for coupled flow and transport problems with applications in oil reservoir simulations

a posteriori analysis of an iterative multi discretization method for reaction diffusion systems abstract this paper is concerned with the accurate computational error estimation of numerical solutions of multi scale multi physics systems of reaction diffusion equations such systems can present significantly different temporal and spatial scales within the components of the model indicating the use of independent discretizations for different components however multi discretization can have significant effects on accuracy and stability we perform an adjoint based analysis to derive asymptotically accurate a posteriori error estimates for a user defined quantity of interest these estimates account for leading order contributions to the error arising from numerical solution of each component an error due to incomplete iteration an error due to linearization and for errors arising due to the projection of solution components between different spatial meshes several numerical examples with various settings are given to demonstrate the performance of the error estimators