最小二乘估计关于误差分布的稳健性

对于设计矩阵$X$是列降秩的线性统计模型, 本文讨论了最小二乘估计关于误差分布的稳健性, 给出了误差分布的最大类, 使得误差项的分布在此范围内变动时, 最小二乘估计在均方误差矩阵准则下是最优估计.     

Panel模型中两步估计的优良性

本文研究Panel模型中未知参数的估计问题，给出了两步估计的协方差的准确表达式．用均方误差作为度量估计的优劣标准，我们建立了两步估计优于Within估计和最小二乘估计的充要条件．特别我们获得了两步估计优于Within估计的简单充分条件．一般说来，对于中等数量的样本容量，两步估计就优于Within估计，类似的结论对Between估计或最小二乘估计也成立．     

偏最小二乘回归的应用效果分析

本文介绍了偏最小二乘回归 (PLS)的建模方法 ,比较了PLS与普通最小二乘回归 (OLS)及主成分回归的应用效果 ,并总结了PLS回归的基本特点 .     

岭估计优于最小二乘估计的条件

本文讨论在均方误差意义下岭估计优于最小二乘估计的问题，给出了岭估计优于小最小二乘估计的必要条件及较一般的充分条件。     

两个多重相关变量组的统计分析(3)(偏最小二乘回归与PLS过程)

本文用PLS过程建立多因变量的偏最小二乘回归模型 ,并用具体例子对最小二乘回归(MLR)、主成分回归 (PCK)和偏最小二乘回归 (PLS)进行比较     

残差自回归半参数模型的参数估计

研究了残差自回归半参数模型的参数估计,运用广义最小二乘法估计了参数部分．用随机模拟说明了运用广义最小二乘（GLSE）估计出的参数部分优于运用普通最小二乘法（OKSE）得到的估计．     

两级抽样回归模型中估计与检验的稳健性

对于两级抽样(two-stage sampling)回归模型,协方差阵含有未知的类内相关系数(intraclustercorrelation)ρ本文研究在设计阵满足何种条件时,回归系数的估计与F-检验不受ρ的影响。即估计与F-检验关于协方差阵具有稳健性。本文对最小二乘估计与似然比F-检验统计量的稳健性分别给出了充要条件、充分条件和必要条件。     

恒加试验中几种线性无偏估计及其比较

在恒加试验中加速方程的二个系数a与b的估计最为重要,常用的加权最小二乘估计(?)与(?)在线性无偏估计类中并不是方差最小的。本文指出,这是由于忽视某些中间估计的恒相关性而使方差增大,考虑这些相关性之后,可以给出a与b的BLUE的简化算法,本文还对a与b设计一种新的加权最小二乘估计,其方差接近最小,而计算较为简便,最后,还给出二种加权最小二乘估计分别与BlUE的相对效率的下界,一个数值例子说明上述各种比较的效果。     

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。     

生长曲线模型中协差阵的最优非负估计

本文给出了一个判定非负定阵的新方法,完成了生长曲线模型中误差协差阵非负估计理论的下列工作:(1)最优估计存在的充要条件及存在时的显示表达;(2)任意二次估计为最优估计的充要条件,作为推论给出了最小二乘估计为最优非负估计的充要条件;(3)给出了一个优于最小二乘估计的新估计.     

Generalized least squares estimation of the functional multivariate linear errors-in-variables model

Estimators of the parameters of the functional multivariate linear errors-in-variables model are obtained by the application of generalized least squares to the sample matrix of mean squares and products. The generalized least squares estimators are shown to be consistent and asymptotically multivariate normal. Relationships between generalized least squares estimation of the functional model and of the structural model are demonstrated. It is shown that estimators constructed under the assumption of normal x are appropriate for fixed x.     

Improving Penalized Least Squares through Adaptive Selection of Penalty and Shrinkage

Estimation of the mean function in nonparametric regression is usefully separated into estimating the means at the observed factor levels—a one-way layout problem—and interpolation between the estimated means at adjacent factor levels. Candidate penalized least squares (PLS) estimators for the mean vector of a one-way layout are expressed as shrinkage estimators relative to an orthogonal regression basis determined by the penalty matrix. The shrinkage representation of PLS suggests a larger class of candidate monotone shrinkage (MS) estimators. Adaptive PLS and MS estimators choose the shrinkage vector and penalty matrix to minimize estimated risk. The actual risks of shrinkage-adaptive estimators depend strongly upon the economy of the penalty basis in representing the unknown mean vector. Local annihilators of polynomials, among them difference operators, generate penalty bases that are economical in a range of examples. Diagnostic techniques for adaptive PLS or MS estimators include basis-economy plots and estimates of loss or risk.     

An efficient generalized least squares algorithm for periodic trended regression with autoregressive errors

Time series data with periodic trends like daily temperatures or sales of seasonal products can be seen in periods fluctuating between highs and lows throughout the year. Generalized least squares estimators are often computed for such time series data as these estimators have minimum variance among all linear unbiased estimators. However, the generalized least squares solution can require extremely demanding computation when the data is large. This paper studies an efficient algorithm for generalized least squares estimation in periodic trended regression with autoregressive errors. We develop an algorithm that can substantially simplify generalized least squares computation by manipulating large sets of data into smaller sets. This is accomplished by coining a structured matrix for dimension reduction. Simulations show that the new computation methods using our algorithm can drastically reduce computing time. Our algorithm can be easily adapted to big data that show periodic trends often pertinent to economics, environmental studies, and engineering practices.     

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??In this paper, we construct a generalized spatial panel data model with two-way error components where the spatial correlation also exist in the individual effects. Based on the methods of the generalized moment estimate and the two-step least square estimate, we look for the best instrumental variable, fit generalized moments and the weighted matrix to discuss the estimator of the parameters, and prove the consistent of the estimators. Monte Carlo experiments show that the weighted generalized moment estimators are better than the unweighted generalized moment estimators, and the estimate effect of feasible generalized two stages least squares estimators is good.     

Multiple Penalty Regression: Fitting and Extrapolating a Discrete Incomplete Multi-way Layout

The d iscrete multi-way layout is an abstract data type associated with regression, experimental designs, digital images or videos, spatial statistics, gene or protein chips, and more. The factors influencing response can be nominal or ordinal. The observed factor level combinations are finitely discrete and often incomplete or irregularly spaced. This paper develops low risk biased estimators of the means at the observed factor level combinations; and extrapolates the estimated means to larger discrete complete layouts. Candidate penalized least squares (PLS) estimators with multiple quadratic penalties express competing conjectures about each of the main effects and interactions in the analysis of variance decomposition of the means. The candidate PLS estimator with smallest estimated quadratic risk attains, asymptotically, the smallest risk over all candidate PLS estimators. In the theoretical analysis, the dimension of the regression space tends to infinity. No assumptions are made about the unknown means or about replication.     

Asymptotic properties of the least squares estimators of the parameters of the chirp signals

Chirp signals are quite common in different areas of science and engineering. In this paper we consider the asymptotic properties of the least squares estimators of the parameters of the chirp signals. We obtain the consistency property of the least squares estimators and also obtain the asymptotic distribution under the assumptions that the errors are independent and identically distributed. We also consider the generalized chirp signals and obtain the asymptotic properties of the least squares estimators of the unknown parameters. Finally we perform some simulations experiments to see how the asymptotic results behave for small sample and the performances are quite satisfactory.     

Double Shrinkage Estimation of Common Coefficients in Two Regression Equations with Heteroscedasticity

The problem of estimating the common regression coefficients is addressed in this paper for two regression equations with possibly different error variances. The feasible generalized least squares (FGLS) estimators have been believed to be admissible within the class of unbiased estimators. It is, nevertheless, established that the FGLS estimators are inadmissible in light of minimizing the covariance matrices if the dimension of the common regression coefficients is greater than or equal to three. Double shrinkage unbiased estimators are proposed as possible candidates of improved procedures.     

An overview on the shrinkage properties of partial least squares regression

The aim of this paper is twofold. In the first part, we recapitulate the main results regarding the shrinkage properties of partial least squares (PLS) regression. In particular, we give an alternative proof of the shape of the PLS shrinkage factors. It is well known that some of the factors are >1. We discuss in detail the effect of shrinkage factors for the mean squared error of linear estimators and argue that we cannot extend the results to PLS directly, as it is nonlinear. In the second part, we investigate the effect of shrinkage factors empirically. In particular, we point out that experiments on simulated and real world data show that bounding the absolute value of the PLS shrinkage factors by 1 seems to leads to a lower mean squared error.     

Efcient Estimation of Varying Coefcient Seemly Unrelated Regression Model

In this paper,we propose a class of varying coefcient seemingly unrelated regression models,in which the errors are correlated across the equations.By applying the series approximation and taking the contemporaneous correlations into account,we propose an efcient generalized least squares series estimation for the unknown coefcient functions.The consistency and asymptotic normality of the resulting estimators are established.In comparison with the ordinary least squares ones,the proposed estimators are more efcient with smaller asymptotical variances.Some simulation studies and a real application are presented to demonstrate the finite sample performance of the proposed methods.In addition,based on a B-spline approximation,we deduce the asymptotic bias and variance of the proposed estimators.     

Generalized least squares and maximum likelihood estimations of multivariate polychoric correlations

This paper investigates the generalized least squares estimation and the maximum likelihood estimation of the parameters in a multivariate polychoric correlations model, based on data from a multidimensional contingency table. Asymptotic properties of the estimators are discussed. An iterative procedure based on the Gauss-Newton algorithm is implemented to produce the generalized least squares estimates and the standard errors estimates. It is shown that via an iteratively reweighted method, the algorithm produces the maximum likelihood estimates as well. Numerical results on the finite sample behaviors of the methods are reported.