带有不完全椭球约束的生长曲线模型中线性估计的可容许性

对于带有不完全椭球约束的生长曲线模型Y=XBZ+ε,ε~(0,σ2VI),X(B-B0)Z′NZ(B-B0)′X′≤σ2In,本文在矩阵损失函数(d-KBL)(d-KBL)′下给出了KBL在类齐次线性估计类LH与非齐次线性估计类LI中可容许的充要条件.本文的结果表明线性估计在非齐次线性估计类中的可容许性与椭球的中心B0无关,而齐次线性估计在齐次线性估计类中的可容许性与B0有关.     

Asymptotically optimal estimation in the linear regression problem in the case of violation of some classical assumptions

We consider the problem of estimating the unknown parameters of linear regression in the case when the variances of observations depend on the unknown parameters of the model. A two-step method is suggested for constructing asymptotically linear estimators. Some general sufficient conditions for the asymptotic normality of the estimators are found, and an explicit form is established of the best asymptotically linear estimators. The behavior of the estimators is studied in detail in the case when the parameter of the regression model is one-dimensional.     

Estimation of location and scale parameters for the Burr XII distribution using generalized order statistics

The minimum variance linear unbiased estimators (MVLUE), the best linear invariant estimators (BLIE) and the maximum likelihood estimators (MLE) based on n-selected generalized order statistics are presented for the parameters of the Burr XII distribution.     

Minimax estimator of regression coefficient in normal distribution under balanced loss function

This article investigates linear minimax estimators of regression coefficient in a linear model with an assumption that the underlying distribution is a normal one with a nonnegative definite covariance matrix under a balanced loss function. Some linear minimax estimators of regression coefficient in the class of all estimators are obtained. The result shows that the linear minimax estimators are unique under some conditions.     

Admissibility of linear estimators with respect to inequality constraints under matrix loss function

In this paper we investigate the admissibility of linear estimators in the multivariate linear model with respect to inequality constraints under matrix loss function. The necessary and sufficient conditions for a linear estimator to be admissible in the class of homogeneous linear estimators and the class of inhomogeneous linear estimators are obtained, respectively.     

秩亏线性模型中的一个新的线性有偏估计类

本文基于最优线性最小偏差估计的谱分解,定义了秩亏线性模型未知参数的一个新的线性有偏估计类,并讨论了它的许多重要性质,通过选取偏参数的适当形式,构造了许多很有意义的线性有偏估计,最后,给出了一个算例。     

Orthoregressive estimates for the parameters of systems of linear difference equations

The problem of estimating the parameters of linear difference systems of equations from the observations of the segments of solutions with additive stochastic perturbations is considered. The methods of multivariate orthogonal regression are applied to obtain the estimators. The results of comparative study of the methods are exposed from the standpoint of information on linear constraints in observations. The properties of the estimators in the limit cases of a gross sample are studied. For small perturbations, a scheme for comparison of estimators by linear approximations is proposed.     

线性混合效应模型中方差分量的估计

本文首先研究了含三个方差分量的线性混合随机效应模型改进的ANOVA估计, 此估计在均方损失下一致优于ANOVA估计. 由于这些方差估计取负值的概率大于零, 对得到的估计在某非负点采用截尾的方法得到非负估计是一种常用的方法. 对文章中提出的估计, 研究了此估计在某非负点截尾之后得到的估计在均方损失意义下优于截尾之前的估计的充分条件, 同时给出ANOVA估计在截尾之后优于它本身的充分条件, 而且将得到的结论推广到更一般的线性混合随机效应模型.     

All admissible linear estimators of a regression coefficient under a balanced loss function

Admissibility of linear estimators of a regression coefficient in linear models with and without the assumption that the underlying distribution is normal is discussed under a balanced loss function. In the non-normal case, a necessary and sufficient condition is given for linear estimators to be admissible in the space of homogeneous linear estimators. In the normal case, a sufficient condition is provided for restricted linear estimators to be admissible in the space of all estimators having finite risks under the balanced loss function. Furthermore, the sufficient condition is proved to be necessary in the normal case if additional conditions are assumed.     

A posteriori estimators for nonlinear elliptic partial differential equations

Many works have reported results concerning the mathematical analysis of the performance of a posteriori error estimators for the approximation error of finite element discrete solutions to linear elliptic partial differential equations. For each estimator there is a set of restrictions defined in such a way that the analysis of its performance is made possible. Usually, the available estimators may be classified into two types, i.e., the implicit estimators (based on the solution of a local problem) and the explicit estimators (based on some suitable norm of the residual in a dual space). Regarding the performance, an estimator is called asymptotically exact if it is a higher-order perturbation of a norm of the exact error. Nowadays, one may say that there is a larger understanding about the behavior of estimators for linear problems than for nonlinear problems. The situation is even worse when the nonlinearities involve the highest derivatives occurring in the PDE being considered (strongly nonlinear PDEs). In this work we establish conditions under which those estimators, originally developed for linear problems, may be used for strongly nonlinear problems, and how that could be done. We also show that, under some suitable hypothesis, the estimators will be asymptotically exact, whenever they are asymptotically exact for linear problems. Those results allow anyone to use the knowledge about estimators developed for linear problems in order to build new reliable and robust estimators for nonlinear problems.     

不等式约束下线性模型中线性估计的可容许性

研究了线性模型在不等式约束条件下齐次和非齐次线性估计的可容许性,刻画了两者之间的关系,得到了不等式约束条件下非齐次线性估计可容许性的充要条件．     

Safe and tight linear estimators for global optimization

Global optimization problems are often approached by branch and bound algorithms which use linear relaxations of the nonlinear constraints computed from the current variable bounds. This paper studies how to derive safe linear relaxations to account for numerical errors arising when computing the linear coefficients. It first proposes two classes of safe linear estimators for univariate functions. Class-1 estimators generalize previously suggested estimators from quadratic to arbitrary functions, while class-2 estimators are novel. When they apply, class-2 estimators are shown to be tighter theoretically (in a certain sense) and almost always tighter numerically. The paper then generalizes these results to multivariate functions. It shows how to derive estimators for multivariate functions by combining univariate estimators derived for each variable independently. Moreover, the combination of tight class-1 safe univariate estimators is shown to be a tight class-1 safe multivariate estimator. Finally, multivariate class-2 estimators are shown to be theoretically tighter (in a certain sense) than multivariate class-1 estimators.     

部分线性变系数模型中估计的渐进正态性

作为部分线性模型与变系数模型的推广,部分线性变系数模型是一类应用非常广泛的模型,本文基于Profile最小二乘方法给出了模型中参数分量与非参数分量的估计,并在异方差情形下证明了这些估计的渐进正态性.     

ADMISSIBILITY OF LINEAR ESTIMATORS IN A GROWTH CURVE MODEL SUBJECT TO AN INCOMPLETE ELLIPSOIDAL RESTRICTION

This article considers the admissibility of the linear estimators for the regression coefficients in the growth curve model subject to an incomplete ellipsoidal restriction. The necessary and sufficient conditions for linear estimators to be admissible in classes of the homogeneous and non-homogeneous linear estimators, respectively, are obtained under the quadratic loss function. They are generalizations of some existing results in literature.     

Estimators of scale parameters in linear regression

This note discusses the asymptotic distribution of two scale and location invariant estimators of two scale parameters in the multiple linear regression model. Both of these estimators need an initial estimator of the regression parameter vector. The asymptotic distribution of one of these estimators does not depend on this initial estimator. Both of these estimators are useful in the computation of scale and translation invariant adaptive estimators and M-estimators of the regression parameter vector.     

Explicit estimators of parameters in the Growth Curve model with linearly structured covariance matrices

Estimation of parameters in the classical Growth Curve model, when the covariance matrix has some specific linear structure, is considered. In our examples maximum likelihood estimators cannot be obtained explicitly and must rely on optimization algorithms. Therefore explicit estimators are obtained as alternatives to the maximum likelihood estimators. From a discussion about residuals, a simple non-iterative estimation procedure is suggested which gives explicit and consistent estimators of both the mean and the linear structured covariance matrix.     

Estimation of covariance matrices in fixed and mixed effects linear models

The estimation of the covariance matrix or the multivariate components of variance is considered in the multivariate linear regression models with effects being fixed or random. In this paper, we propose a new method to show that usual unbiased estimators are improved on by the truncated estimators. The method is based on the Stein–Haff identity, namely the integration by parts in the Wishart distribution, and it allows us to handle the general types of scale-equivariant estimators as well as the general fixed or mixed effects linear models.     

带有不完全椭球约束的线性模型中线性估计的可容许性

本文刻划了线性模型（Ｙ，Ｘβ，σ２Ｖ，Ｖ≥０）在不完全椭球约束：（β－β０）’Ｎ（β－ β Ｐ０）≤σ２，Ｎ ≥ ０下的线性估计的可容许性．本文的结果显示了一个有趣的现象，即一个线性估计在全体线性估计所组成的类中的可容许性与椭球的中心β０无关，而在全体齐次线性估计所组成的类中的可容许性与β０有关．     

Simple and efficient improvements of multivariate local linear regression

This paper studies improvements of multivariate local linear regression. Two intuitively appealing variance reduction techniques are proposed. They both yield estimators that retain the same asymptotic conditional bias as the multivariate local linear estimator and have smaller asymptotic conditional variances. The estimators are further examined in aspects of bandwidth selection, asymptotic relative efficiency and implementation. Their asymptotic relative efficiencies with respect to the multivariate local linear estimator are very attractive and increase exponentially as the number of covariates increases. Data-driven bandwidth selection procedures for the new estimators are straightforward given those for local linear regression. Since the proposed estimators each has a simple form, implementation is easy and requires much less or about the same amount of effort. In addition, boundary corrections are automatic as in the usual multivariate local linear regression.     

Admissible linear estimators in restricted linear models

Necessary and sufficient conditions are established for a linear estimator to be admissible among the set of all homogeneous and inhomogeneous, linear estimators under a linear model with the vector of parameters subject to linear restrictions. These conditions are then utilized to characterize influence that restrictions involved in a linear model have on the class of admissible linear estimators.