二次损失下随机回归系数和参数的线性Minimax估计

对带有随机效应的一般线性模型,本文提出了随机回归系数和参数线性组合的Minimax估计问题. 在二次损失下,研究了线性估计的极小极大性.关于适当的假设,得到了可估函数的唯一线性Mjnimax 估计.     

二次损失下随机回归系数和参数的线性Minimax估计

对带有随机效应的一般线性模型,本文提出了随机回归系数和参数线性组合的Minimax估计问题.在二次损失下,研究了线性估计的极小极大性.关于适当的假设,得到了可估函数的唯一线性Minimax估计.     

不等式约束下线性模型中线性估计的可容许性

本文研究了带有不等式约束的多指标线性模型中线性估计的可容许性.利用矩阵论的相关知识,在矩阵损失下得到了齐次线性估计在齐次线性估计类中是可容许的充要条件,以及非齐次线性估计在非齐次线性估计类中是可容许的若干条件,推广了不等式约束下可容许性的相关结果.     

带有不完全信息的随机截尾广义线性模型的中偏差

本文介绍了随机截尾的带有不完全信息的广义线性模型,并在一定条件下运用Taylor渐近展开方法得到了此模型的极大似然估计的中偏差.     

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.     

平衡线性混合模型方差分量几种估计的优良性

对于平衡线性混合模型,本文提出了一组易验证的条件,在此条件下,方差分量的谱分解估计、方差分析估计和最小范数二次无偏估计都相等且为一致最小方差无偏估计.同时证明了在此条件下,似然方程和限制似然方程都有显式解,还给出了许多满足这组条件的平衡线性混合模型的例子.     

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.     

独立约束条件下线性模型的参数估计

对线性回归的未知参数估计问题,在某些种假设的条件下已有结论,对有约束条件的情况下,线性回归模型中参数估计如何,本文给出了带有独立的约束条件下线性回归模型中参数β的最小二乘估计。     

序贯k-out-of-n系统在序约束下参数的估计和算法

本文主要研究带有协变量的序贯k-out-of-n模型.我们假定给定协变量寿命的分布是指数分布,对指数分布的刻度参数建立了对数线性模型.研究了在序约束下模型参数的最大似然估计及最大似然估计量的性质,并且给出了最大似然估计的具体算法并进行了模拟.     

具有相关误差的多元线性模型的更新方程

已知的线性模型的更新方程是在对模型加了不相关误差结构的约束, 或只对带有固定参数的一元线性模型考虑的. 本文考虑具有相关误差的多元线性模型下的更新方程, 给出了在补充参数, 数据或指标时, 未知参数阵的最佳线性无偏估计及残积阵的更新方程. 公式适用于固定参数与随机参数两种情形.     

Normal Linear Regression Models With Recursive Graphical Markov Structure

A multivariate normal statistical model defined by the Markov properties determined by an acyclic digraph admits a recursive factorization of its likelihood function (LF) into the product of conditional LFs, each factor having the form of a classical multivariate linear regression model (≡WMANOVA model). Here these models are extended in a natural way to normal linear regression models whose LFs continue to admit such recursive factorizations, from which maximum likelihood estimators and likelihood ratio (LR) test statistics can be derived by classical linear methods. The central distribution of the LR test statistic for testing one such multivariate normal linear regression model against another is derived, and the relation of these regression models to block-recursive normal linear systems is established. It is shown how a collection of nonnested dependent normal linear regression models (≡Wseemingly unrelated regressions) can be combined into a single multivariate normal linear regression model by imposing a parsimonious set of graphical Markov (≡Wconditional independence) restrictions.     

线性模型中F-检验的稳健性

本文讨论了一般线性模型中关于均值参数β的线性假设基于广义最小二乘估计的F-检验统计量的稳健性问题.主要研究了当误差的协方差矩阵含有参数时,设计阵可以列降秩情况下的F-检验统计量的稳健性,得到了F(V(θ))为该假设下F-检验统计量的误差协方差矩阵的最大类.并讨论了分块线性模型中,关于分块参数的线性假设的F-检验统计量的稳健性.     

Limiting Behavior of M-Estimators of Regression Coefficients in High Dimensional Linear Models I. Scale Dependent Case

Asymptotics of M-estimators of the regression coefficients in linear models (both scale-variant and scale-invariant) when the number of regression coefficients tends to infinity as the sample size increases are investigated The main purpose of this study is to establish the asymptotic properties under weaker conditions than usually assumed, especially to relax the restrictions on the order of the dimension. Also, the conditions assumed and the results obtained seem easy to be extended to the multivariate linear models. In the first part of the paper, the asymptotic behavior of the ordinary (i.e., not scale-invariant) M-estimates is considered.     

Pseudospectra Analysis, Nonlinear Eigenvalue Problems, and Studying Linear Systems with Delays

Time delays occur naturally in many physical and social systems. Computer simulations of such systems require that models of these systems be stable, and perhaps even passive, if several such systems are to be joined together in the simulation. We present a visual procedure for studying the stability and passivity of such systems. This procedure uses ideas from pseudospectra analysis. It is applicable to systems of linear, delay-differential-algebraic equations. There are no a priori restrictions on the types or sizes of the delays. No approximations to the original system are made. All approximations are confined to the grid used in the visualization procedure, and the procedure parallelizes readily. We apply this procedure to the study of the stability and passivity of proposed models for simulations of the behavior of currents and voltages in packaged VLSI interconnects (wires and planes) in computers. Simulations are required to verify that internal electromagnetic fields do not significantly delay or distort circuit signals.This revised version was published online in October 2005 with corrections to the Cover Date.     

带线性约束的回归模型参数估计的新研究

针对一般带约束的最小二乘估计(ORLSE)在参数估计中处理复共线性的不足,引入随机线性约束,提出了约束k-d估计方法。在均方误差(MSE)下,讨论了它的性质,得到了四个主要结果,与带约束的最小二乘估计ORLSE、约束岭估计(RRE)和约束型Liu估计比较,得出更好的结论。     

部分线性模型的随机约束岭估计

研究了部分线性回归模型附加有随机约束条件时的估计问题.基于Profile最小二乘方法和混合估计方法提出了参数分量随机约束下的Profile混合估计,并研究了其性质.为了克服共线性问题,构造了参数分量的Profile混合岭估计,并给出了估计量的偏和方差.     

线性模型中的一类随机约束$s$--$K$估计

In this paper, we propose a stochastic restricted s–K estimator in the linear model with additional stochastic linear restrictions by combining the ordinary mixed estimator(OME) with the s–K estimator. It is shown that the proposed estimator is superior to the OME and the s–K estimator under the mean squared error matrix criterion under some conditions. Finally, a numerical example and a Monte Carlo simulation study are given to verify the theoretical results.     

Linear barycentric rational quadrature

Linear interpolation schemes very naturally lead to quadrature rules. Introduced in the eighties, linear barycentric rational interpolation has recently experienced a boost with the presentation of new weights by Floater and Hormann. The corresponding interpolants converge in principle with arbitrary high order of precision. In the present paper we employ them to construct two linear rational quadrature rules. The weights of the first are obtained through the direct numerical integration of the Lagrange fundamental rational functions; the other rule, based on the solution of a simple boundary value problem, yields an approximation of an antiderivative of the integrand. The convergence order in the first case is shown to be one unit larger than that of the interpolation, under some restrictions. We demonstrate the efficiency of both approaches with numerical tests.     

线性模型下F-检验最优的误差协方差结构

文献中回归参数线性假设的F-检验统计量主要包括基于广义最小二乘估计F- 统计量F(θ),基于最小二乘估计的F-统计量FLSE以及Wu C．F．J．等于1988年提出的调整的F-统计量FA(θ)．其中后两者因形式简单而常常被广泛采用．本文主要研究了FA(θ)和FLSE的最优性,并分别获得了FA(θ)=F(θ)和ELSE=F(θ)的充要条件．最后,我们将所得的结果应用到医药领域的两类重要模型．     

Estimating Frailty Models via Poisson Hierarchical Generalized Linear Models

Frailty models extend proportional hazards models to multivariate survival data. Hierarchical-likelihood provides a simple unified framework for various random effect models such as hierarchical generalized linear models, frailty models, and mixed linear models with censoring. Wereview the hierarchical-likelihood estimation methods for frailty models. Hierarchical-likelihood for frailty models can be expressed as that for Poisson hierarchical generalized linear models. Frailty models can thus be fitted using Poisson hierarchical generalized linear models. Properties of the new methodology are demonstrated by simulation. The new method reduces the bias of maximum likelihood and penalized likelihood estimates.