平衡损失下回归系数的最优线性无偏估计

在平衡损失函数下得到了回归系数的最优线性无偏估计,结果表明平衡损失下的最优线性无偏估计就是线性模型中回归系数的最小二乘估计.     

加权平衡损失函数下回归系数的最佳线性无偏估计

这篇文章我们研究了回归系数的最佳线性无偏估计. 在加权平衡损失函数下, 我们得到了回归系数的最佳线性无偏估计. 同时提出了度量最佳线性无偏估计和最小二乘估计的相对效率. 并且我们给出了它们的上下界.     

两个线性模型间最优线性无偏预测的等价性

设M1和M2是两个带有预测量的线性模型,通过使用矩阵秩方法,本文给出了模型M1下预测量的最优线性无偏预测同时也是模型M2下的最优线性无偏预测的充分必要条件.作为这个结果的应用,我们给出了两个线性混合模型间最优线性无偏预测等价性的充分必要条件.     

一般线性模型下方差最小范数二次无偏估计的稳健性

本文给出了一般线性模型下,由最小二乘得到的方差估计与最小范数二次无偏估计相等的充分必要条件,并且当Gauss-Markov估计与最小二乘估计相等时,可以得到一个简单的等价条件。     

一类线性模型中Bayes估计的优良性

本文研究了一类线性模型中参数的Bayes线性无偏估计的优良性.利用矩阵论的相关知识,分别在平衡损失准则和均方误差阵准则下,得到了Bayes线性无偏估计优于广义最小二乘估计的条件.     

一类线性模型下最优线性无偏估计的存在性

考虑包含如方差分量模型、似乎不相关回归方程模型、增长曲线模型和扩充的增长曲线模型等众多常见模型的一类较广泛的线性模型。对模型中误差向量的分布不作假定时,给出了在二次损失或矩阵损失下存在回归系数的线性可估函数的一致最小风险线性无偏估计的充分必要条件。     

多元线性模型中随机回归系数和参数的最优估计

本文研究了一般的随机效应多元线性模型中线性可估函数的最优线性无偏估计。特别地 ,考虑了一类特殊的估计 :Φ-线性估计 ,给出了 Φ-线性可估函数和最优 Φ—线性无偏估计的定义。得到了 Φ-线性可估函数的最优Φ—线性无偏估计 ,并证明了它在几乎处处意义下的唯一性     

多元线性模型中Var■的Jack Knife估计

提出多元异协差阵模型,即对于B的l.s.e,给出Var()的省d项的加权Jack Knife估计,在适当条件下证实这一估计的渐近无偏稳健性以及一致稳健性,(A.U稳健性及C稳健性),对省1项的几种Jack Knife估计作出比较,并得出这些估计具A.U稳健性与C-稳健性的充分必要条件。     

分块奇异线性模型及其导出的奇异线性模型间的最小范数二次无偏估计等价性研究

本文考虑一般线性模型A=(y,X1β1 X2β2,σ^2V)及其导出线性模型，其中V是已知的非负定矩阵，X=(X1：X2)是已知的设计矩阵，给出了线性模型A及其导出线性模型间最小范数二次无偏估计间差的表达式，更进一步，建立了线性模型A及其导出线性模型间最小范数二次无偏估计相等的充分必要条件。     

二次损失下随机回归系数和参数的线性估计是可容许的充要条件

本文对于一般的随机效应线性模型(包括混合效应线性模型),在二次损失函数下给出了随机回归系数和参数的线性可估函数的齐次线性估计(线性估计)在齐次线性估计类(线性估计类)中可容许的充分必要条件.     

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.     

Time series regression models with locally stationary disturbance

Time series linear regression models with stationary residuals are a well studied topic, and have been widely applied in a number of fields. However, the stationarity assumption on the residuals seems to be restrictive. The analysis of relatively long stretches of time series data that may contain changes in the spectrum is of interest in many areas. Locally stationary processes have time-varying spectral densities, the structure of which smoothly changes in time. Therefore, we extend the model to the case of locally stationary residuals. The best linear unbiased estimator (BLUE) of vector of regression coefficients involves the residual covariance matrix which is usually unknown. Hence, we often use the least squares estimator (LSE), which is always feasible, but in general is not efficient. We evaluate the asymptotic covariance matrices of the BLUE and the LSE. We also study the efficiency of the LSE relative to the BLUE. Numerical examples illustrate the situation under locally stationary disturbances.     

New insights into best linear unbiased estimation and the optimality of least-squares

New results in matrix algebra applied to the fundamental bordered matrix of linear estimation theory pave the way towards obtaining additional and informative closed-form expressions for the best linear unbiased estimator (BLUE). The results prove significant in several respects. Indeed, more light is shed on the BLUE structure and on the working of the OLS estimator under nonsphericalness in (possibly) singular models.     

A robustness study in sampling on successive occasions

Summary In this paper, we have undertaken an investigation covering three occasions in sampling on successive occasions with a view to examining efficiency robustness of the best linear unbiased estimator (BLUE) visa-vis certain other potentially conceivable estimators when the usual correlation model breaks down. We have inferred that the BLUE, is by and large, an efficiency robust estimate in the face of unforeseen deviations from the usual correlation model.     

一般半相依回归系统的协方差改进估计

本文讨论了由两个等阶的回归方程组成的半相依系统,运用协方差改进法获得了参数的一个迭代估计序列,并证明了它的协方差阵已知时,处处收敛到最佳线性无偏估计,同时其协方差阵在矩阵偏序意义下单调性,并且给出了当迭代次数亦趋于无穷时,保证其具有相合性的一个条件。     

任意秩有限总体中无偏预测和估计的构造关系

研究了有限总体均值向量的无偏估计和线性可预测变量的无偏预测之间的关系,利用分块矩阵广义逆直接对加权风险函数进行分解,提出了一种由均值向量的无偏估计来构造无偏预测的新方法,并找到了它们之间的构造关系.特别地,线性可预测变量的最优线性无偏预测(BLUP)可由均值向量的最佳线性无偏估计(BLUE)惟一地表示(有关惟一性在几乎处处意义下理解).     

On a Multiparameter Version of Tukey's Linear Sensitivity Measure and its Properties

A multiparameter version of Tukey's (1965, Proc. Nat. Acad. Sci. U.S.A., 53, 127–134) linear sensitivity measure, as a measure of informativeness in the joint distribution of a given set of random variables, is proposed. The proposed sensitivity measure, under some conditions, is a matrix which is non-negative definite, weakly additive, monotone and convex. Its relation to Fisher information matrix and the best linear unbiased estimator (BLUE) are investigated. The results are applied to the location-scale model and it is observed that the dispersion matrix of the BLUE of the vector location-scale parameter is the inverse of the sensitivity measure. A similar property was established by Nagaraja (1994, Ann. Inst. Statist. Math., 46, 757–768) for the single parameter case when applied to the location and scale models. Two illustrative examples are included.     

Sampling designs for regression coefficient estimation with correlated errors

The problem of estimating regression coefficients from observations at a finite number of properly designed sampling points is considered when the error process has correlated values and no quadratic mean derivative. Sacks and Ylvisaker (1966,Ann. Math. Statist.,39, 66–89) found an asymptotically optimal design for the best linear unbiased estimator (BLUE). Here, the goal is to find an asymptotically optimal design for a simpler estimator. This is achieved by properly adjusting the median sampling design and the simpler estimator introduced by Schoenfelder (1978, Institute of Statistics Mimeo Series No. 1201, University of North Carolina, Chapel Hill). Examples with stationary (Gauss-Markov) and nonstationary (Wiener) error processes and with linear and nonlinear regression functions are considered both analytically and numerically.Research supported by the Air Force Office of Scientific Research Contract No. 91-0030.     

Bayes估计的进一步研究及其Pitman最优性

对线性模型参数,讨论了Bayes估计的Pitman最优性,将已有结果进行了改进,去掉了附加条件,证明了在Pitman准则下,Bayes估计一致优于最小二乘估计(LSE),在此基础上,提出了一种基于先验信息的方差分量估计,通过和基于LSE的方差分量估计作比较,证明了新估计是无偏估计且有更小的均方误差．最后,证明了在Pitman准则下生长曲线模型参数的Bayes估计优于最佳线性无偏估计．