Adaptive finite element methods for the identification of distributed parameters in elliptic equation

In this paper, adaptive finite element method is developed for the estimation of distributed parameter in elliptic equation. Both upper and lower error bound are derived and used to improve the accuracy by appropriate mesh refinement. An efficient preconditioned project gradient algorithm is employed to solve the nonlinear least-squares problem arising in the context of parameter identification problem. The efficiency of our error estimators is demonstrated by some numerical experiments.      

Adaptive characteristic finite element approximation of convection–diffusion optimal control problems

In this article, a characteristic finite element approximation of quadratic optimal control problems governed by linear convection–diffusion equations is given. We derive some a posteriori error estimates for both the control and the state approximations, where the control variable is constrained by pointwise inequality. The derived error estimators are then used as an error indicator to guide the mesh refinement. In this sense, they are very important in developing adaptive finite element algorithm for the optimal control problems. Finally, a numerical example is given to validate the efficiency and reliability of the theoretical results. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Error estimators for advection–reaction–diffusion equations based on the solution of local problems

This paper deals with a posteriori error estimates for advection–reaction–diffusion equations. In particular, error estimators based on the solution of local problems are derived for a stabilized finite element method. These estimators are proved to be equivalent to the error, with equivalence constants eventually depending on the physical parameters. Numerical experiments illustrating the performance of this approach are reported.     

错误先验假定下Bayes线性无偏估计的稳健性

本文基于错误的先验假定获得了一般线性模型下可估函数的Bayes线性无偏估计(BLUE), 证明了在均方误差矩阵(MSEM)准则和后验Pitman Closeness (PPC)准则下BLUE相对于最小二乘估计(LSE)的优良性, 并导出了它们的相对效率的界, 从而获得BLUE的稳健性.     

Measuring the efficiency of trigonometric series estimates of a density

Some types of density estimators, particularly those based on trigonometric series, converge reasonably quickly to their limit except in the neighbourhood of one or two singularities. In this situation the mean integrated square error, the traditional measure of the efficiency of a density estimator, is an unsatisfactory measure. The notion of partial mean integrated square error is introduced and used to compare the performance of trigonometric series estimators. The results lead to consideration of some new estimators which have excellent properties from the points of view of both efficiency and ease of computation.     

Second derivative estimation using harmonic analysis

Simulation sensitivity analysis is an important problem for simulation practitioners analyzing complex systems. The significance of this problem has resulted in the development of various gradient estimators that can be used to address this issue. Although higher derivative estimators have been discussed concurrently, less attention has been given to assess the efficiency and feasibility of computing such estimators. In this paper, two second derivative estimators are presented. The first estimators, called the HFD estimators, combine harmonic gradient estimators with finite differences second derivative estimators. The resulting hybrid estimators requireO(p) fewer simulation runs to implement compared to the straightforward finite differences approach, wherep is the number of input parameters in the simulation model. The second estimators, called the HA estimators, incorporate harmonic analysis directly, requiring one or two simulation runs to implement, depending on whether a control variate simulation run is made. Expressions for the bias and the variance of the HFD and the HA estimators (with and without variance reduction techniques) are derived. Optimal mean squared error convergence rates are also discussed. In particular, the convergence rates for both these estimators are shown to be the same, though the computational performance of the HFD estimators is better than that for the HA estimators on anM/M/1 queue simulation model. Computational results for the HFD estimators on an (s, S) inventory system simulation model are also included.     

Optimal Control of Population Dynamics

This paper studies the role of projection algorithms in conditional set membership estimation. These algorithms are known to be suboptimal in terms of the worst-case estimation error. A tight upper bound on the error of central projection estimators and interpolatory projection estimators is computed as a function of the conditional radius of information. Since the radius of information represents the minimum achievable error, the derived bound provides a measure of the reliability level of the suboptimal algorithms. The results are derived in a general deterministic setting, which allows the consideration of linearly parametrized approximations of a compact set of feasible problem elements.     

Modeling matching error and its effect on estimates of census coverage error

"In this paper, we propose a model for investigating the effect of matching error on the estimators of census undercount and illustrate its use for the 1990 [U.S.] census undercount evaluation program. The mean square error [MSE] of the dual system estimator is derived under the proposed model and the components of MSE arising from matching error are defined and explained. Under the assumed model, the effect of matching error on the MSE of the estimator of census undercount is investigated. Finally, a methodology for employing the model for the optimal design of matching error evaluation studies will be illustrated and the form of the estimators will be given."     

Preliminary Test Two-Parameter Estimators Based on W,LR and LM Test-Statistics in a Regression Model

In this paper, we proposed the preliminary test two-parameter estimators based on the Wald (W), the Likelihood Ration (LR) and the Lagrangian Multiplier (LM) tests, when it is suspected that the regression parameter may be restricted to a subspace. The bias and the mean square error (MSE) of the proposed estimators are derived and compared. The conditions of superiority of the proposed estimators are obtained.     

Residual-based a posteriori error estimates of nonconforming finite element method for elliptic problems with Dirac delta source terms

Two residual-based a posteriori error estimators of the nonconforming Crouzeix-Raviart element are derived for elliptic problems with Dirac delta source terms.One estimator is shown to be reliable and efficient,which yields global upper and lower bounds for the error in piecewise W1,p seminorm.The other one is proved to give a global upper bound of the error in Lp-norm.By taking the two estimators as refinement indicators,adaptive algorithms are suggested,which are experimentally shown to attain optimal convergence orders.     

对流扩散方程迎风有限元的自适应方法

本文对二维发展型对流扩散方程的迎风有限元格式给出了显式后验误差估计,证明了真实误差被后验误差估计器上下界定;并通过误差估计器建立了相应的自适应算法,数值例子表明了方法的有效性.     

Restricted estimation in multivariate measurement error regression model

We study a multivariate ultrastructural measurement error (MUME) model with more than one response variable. This model is a synthesis of multivariate functional and structural models. Three consistent estimators of regression coefficients, satisfying the exact linear restrictions have been proposed. Their asymptotic distributions are derived under the assumption of a non-normal measurement error and random error components. A simulation study is carried out to investigate the small sample properties of the estimators. The effect of departure from normality of the measurement errors on the estimators is assessed.     

The a Posteriori Error Estimator of SDG Method for Variable Coefficients Time-Harmonic Maxwell's Equations

In this paper, we study the a posteriori error estimator of SDG method for variable coefficients time-harmonic Maxwell's equations. We propose two a posteriori error estimators, one is the recovery-type estimator, and the other is the residual-type estimator. We first propose the curl-recovery method for the staggered discontinuous Galerkin method (SDGM), and based on the super-convergence result of the postprocessed solution, an asymptotically exact error estimator is constructed. The residual-type a posteriori error estimator is also proposed, and it's reliability and effectiveness are proved for variable coefficients time-harmonic Maxwell's equations. The efficiency and robustness of the proposed estimators is demonstrated by the numerical experiments.     

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Berkson测量误差模型在工业、农业、流行病学、经济学 等领域有广泛的应用. 本文考虑了一类多元超结构Berkson测量误差模型, 给出了该模型中参数的相合估计, 推导了估计的渐近分布, 并把该方法应用到一元超结构Berkson测量误差模型中, 最后给出了模拟结果和实例分析来说明本文所提出的估计方法的表现.     

Optimizing in the class of Fuller modified limited information maximum likelihood estimators

A general class of Fuller modified maximum likelihood estimators are considered. It is shown that this class possesses finite moments. Asymptotic bias and asymptotic mean squared error are derived using small-σ expansions. A simulation study is carried out to compare different estimators in this class with standard estimators.     

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??The Bayes estimators of variance components are derived under weighted square loss function for the balanced one-way classification random effects model with the assumption that variance component has the conjugate prior distribution. The superiorities of the Bayes estimators for variance components to traditional ANOVA estimators are studied in terms of the mean square error (MSE) criterion. Finally, a remark for main results is given.     

Bayesian inference for Pr (Y

《Applied Mathematical Modelling》2014,38(5-6):1698-1709

A posteriori error estimation for fully discrete hierarchic models of elliptic boundary value problems on thin domains

Summary. A posteriori error estimators for fully discrete hierarchic modelling on thin domains are derived and are shown to provide computable upper bounds on the discretization error and on the total error. The estimators are shown to be robust and do not degenerate as the thickness of the domain tends to zero. If the discretization part of the error is negligible, the estimator for the modelling error reduces to the one recently obtained for semi-discrete hierarchical modelling by Babuska and Schwab. Received July 25, 1996 / Revised version received July 31, 1997     

Error Process Indexed by Bandwidth Matrices in Multivariate Local Linear Smoothing

We focus on nonparametric multivariate regression function estimation by locally weighted least squares. The asymptotic behavior for a sequence of error processes indexed by bandwidth matrices is derived. We discuss feasible data-driven consistent estimators minimizing asymptotic mean squared error or efficient estimators reducing asymptotic bias at points where opposite sign curvatures of the regression function are present in different directions.     

Guaranteed a posteriori error estimates for nonconforming finite element approximations to a singularly perturbed reaction–diffusion problem

We derive guaranteed a posteriori error estimates for nonconforming finite element approximations to a singularly perturbed reaction–diffusion problem. First, an abstract a posteriori error bound is derived under a special equilibration condition. Based on conservative flux reconstruction, two error estimators are proposed and provide actual upper error bounds in the usual energy norm without unknown constants, one of which can be directly constructed without solving local Neumann problems and provide practical computable error bounds. The error estimators also provide local lower bounds but with the multiplicative constants dependent on the diffusion coefficient and mesh size, where the constants can be bounded for enough small mesh size comparable with the square root of the diffusion coefficient. By adding edge jumps with weights to the energy norm, two modified error estimators with additional edge tangential jumps are shown to be robust with respect to the diffusion coefficient and provide guaranteed upper bounds on the error in the modified norm. Finally, the performance of the estimators are illustrated by the numerical results.