SUR回归系统系数估计的一些推广结果

文[1]给出了关于相依回归方程系统(SURS)系数最小方差无偏估计(MVLUE)的一些充要条件,本文继续讨论了两类SURS的回归系数的MVLUE的充要条件,并讨论了两步Zellner估计的有限样本性质,从而进一步推广和完善了[1]中的相应结果。     

分块半相依线性回归模型的参数估计

考虑一般的分块半相依线性回归（SUR）模型及其相应的简约模型，给出简约模型下未知回归系数及其可估函数的协方差改进估计仍是分块SUR模型下相应参数的协方差改进估计的一个充要条件．     

简约SUR模型参数的协方差改进估计

考虑了SUR模型及其两个简约模型,给出简约模型下未知回归系数及其可估函数的协方差改进估计,并证明了在一定条件下该估计仍然是相应参数在原模型下的协方差改进估计.     

增长曲线模型回归系数线性估计的泛容许性

本文讨论增长曲线模型回归系数的线性估计的容许性.我们给出了回归系数线性估计的泛容许性定义,并在某些线性估计类中得到了泛容许估计的充要条件.     

平衡损失下约束线性回归模型中回归系数的可容许估计

本文在平衡损失函数下得到等式约束模型中回归系数在齐次(非齐次)估计类中存在可容许估计的充要条件,给出带有不完全椭球约束模型中回归系数的线性估计在一切估计类中为可容许估计的充要条件.     

一类SUR模型参数两步估计的有限样本结果

对于m（3）SUR模型（1），其设计矩阵满足条件（4），本文得到了回归系数βi（i＝1，…，m）的两步Aitken估计的精确协方差表达式，从而获得了两步估计优于LS估计的有限样本性质．特别是，当m＝3时本文结果可以与Revankar（1974）给出的一类两方程SUR模型结果相比较.     

一般增长曲线模型回归系数线性估计的可容许性

在矩阵损失函数下,讨论了一般增长曲线模型中回归系数线性估计的可容许性问题,分别在齐次与非齐次估计类中给出了回归系数的线性估计是可容许估计的充要条件,推广了以往文献的相关结论.     

带约束生长曲线模型线性估计的泛容许性

本文讨论带约束生长曲线模型中回归系数线性估计的泛容许性,给出了回归系数的线性估计在线性估计类中是泛容许估计的充要条件。     

矩阵损失下生长曲线模型中回归系数线性函数的MINIMAX可容许估计

本文在矩阵损失下给出了生长曲线模型中回归系数线性估计在某种线性估计类中是Minimax可容许估计的充要条件     

带有结构变化的线性模型中参数估计的一些结果

本文在一些纯量损失和矩阵损失下研究带有结构变化的正态线性模型中参数的估计问题.分别给出了存在回归系数的一致最小风险无偏(UMRU)估计和一致最小风险同变(UMRE)估计的充要条件.证明了不存在误差方差在仿射变换群下的UMRE估计.导出了回归系数的最小二乘估计的可容许性和极小极大性.     

纵向数据边际模型非参数光滑方法的比较

对于纵向数据边际模型的均值函数, 有很多非参数估计方法, 其中回归样条, 光滑样条, 似乎不相关(SUR)核估计等方法在工作协方差阵正确指定时具有最小的渐近方差. 回归样条的渐近偏差与工作协方差阵无关, 而SUR核估计和光滑样条估计的渐近偏差却依赖于工作协方差阵. 本文主要研究了回归样条, 光滑样条和SUR核估计的效率问题. 通过模拟比较发现回归样条估计的表现比较稳定, 在大多数情况下比光滑样条估计和SUR核估计的效率高.     

增长曲线模型回归系数线性估计的可容许性

该文讨论增长曲线模型中回归系数线性估计的可容许性, 在矩阵损失(d(Y)-KBL)(d(Y)-KBL)' 下, 分别给出了回归系数的齐次与非齐次线性估计是可容许的充要条件, 推广了以往文献的相关结论.     

半参数空间变系数回归模型的Back-Fitting估计

针对半参数空间变系数回归模型给出了一种估计方法-后向拟合估计,该方法可得到模型中常值系数估计量的精确解析表达式,广泛的数值模拟表明所提出的估计方法对估计常值系数具有满意的精度和稳定性,最后,利用该方法分析了一个实际的例子.     

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.     

变系数线性EV模型参数的调整加权最小二乘估计及其渐近性质

研究当结构关系EV(errors-in-variables)模型的系数随某个实变量变化时,如何估计其系数,以及估计的性质如何．采用调整的加权最小二乘方法估计结构关系EV模型的变系数,证明在比较弱的条件下用这种方法得到的估计具有强相合性和渐近正态性,模拟研究表明所提估计性质良好．     

Existence of the uniformly minimum risk equivariant estimators of parameters in a class of normal linear models

In this paper, we study the existence of the uniformly minimum risk equivariant (UMRE) estimators of parameters in a class of normal linear models, which include the normal variance components model, the growth curve model, the extended growth curve model, and the seemingly unrelated regression equations model, and so on. The necessary and sufficient conditions are given for the existence of UMRE estimators of the estimable linear functions of regression coefficients, the covariance matrixV and (trV)^α, where α > 0 is known, in the models under an affine group of transformations for quadratic losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model, the conclusions given in literature for estimating regression coefficients can be derived by applying the general results in this paper, and the sufficient conditions for non-existence of UMRE estimators ofV and tr(V) are expanded to be necessary and sufficient conditions. In addition, the necessary and sufficient conditions that there exist UMRE estimators of parameters in the variance components model are obtained for the first time.     

Existence conditions for the uniformly minimum risk unbiased estimators in a class of linear models

This paper studies the existence of the uniformly minimum risk unbiased (UMRU) estimators of parameters in a class of linear models with an error vector having multivariate normal distribution or t-distribution, which include the growth curve model, the extended growth curve model, the seemingly unrelated regression equations model, the variance components model, and so on. The necessary and sufficient existence conditions are established for UMRU estimators of the estimable linear functions of regression coefficients under convex losses and matrix losses, respectively. Under the (extended) growth curve model and the seemingly unrelated regression equations model with normality assumption, the conclusions given in the literature can be derived by applying the general results in this paper. For the variance components model, the necessary and sufficient existence conditions are reduced as terse forms.     

Mixtures of semiparametric varying coefficient models for longitudinal data with nonignorable dropout

Informative dropout often arise in longitudinal data. In this paper we propose a mixture model in which the responses follow a semiparametric varying coefficient random effects model and some of the regression coefficients depend on the dropout time in a non-parametric way. The local linear version of the profile-kernel method is used to estimate the parameters of the model. The proposed estimators are shown to be consistent and asymptotically normal, and the finite performance of the estimators is evaluated by numerical simulation.     

Efficient parameter estimation via modified Cholesky decomposition for quantile regression with longitudinal data

It is well known that specifying a covariance matrix is difficult in the quantile regression with longitudinal data. This paper develops a two step estimation procedure to improve estimation efficiency based on the modified Cholesky decomposition. Specifically, in the first step, we obtain the initial estimators of regression coefficients by ignoring the possible correlations between repeated measures. Then, we apply the modified Cholesky decomposition to construct the covariance models and obtain the estimator of within-subject covariance matrix. In the second step, we construct unbiased estimating functions to obtain more efficient estimators of regression coefficients. However, the proposed estimating functions are discrete and non-convex. We utilize the induced smoothing method to achieve the fast and accurate estimates of parameters and their asymptotic covariance. Under some regularity conditions, we establish the asymptotically normal distributions for the resulting estimators. Simulation studies and the longitudinal progesterone data analysis show that the proposed approach yields highly efficient estimators.     

Comparisons among some estimators in misspecified linear models with multicollinearity

In this paper we deal with comparisons among several estimators available in situations of multicollinearity (e.g., the r-k class estimator proposed by Baye and Parker, the ordinary ridge regression (ORR) estimator, the principal components regression (PCR) estimator and also the ordinary least squares (OLS) estimator) for a misspecified linear model where misspecification is due to omission of some relevant explanatory variables. These comparisons are made in terms of the mean square error (mse) of the estimators of regression coefficients as well as of the predictor of the conditional mean of the dependent variable. It is found that under the same conditions as in the true model, the superiority of the r-k class estimator over the ORR, PCR and OLS estimators and those of the ORR and PCR estimators over the OLS estimator remain unchanged in the misspecified model. Only in the case of comparison between the ORR and PCR estimators, no definite conclusion regarding the mse dominance of one over the other in the misspecified model can be drawn.