Minimax multivariate empirical Bayes estimators under multicollinearity

In this paper we consider the problem of estimating the matrix of regression coefficients in a multivariate linear regression model in which the design matrix is near singular. Under the assumption of normality, we propose empirical Bayes ridge regression estimators with three types of shrinkage functions, that is, scalar, componentwise and matricial shrinkage. These proposed estimators are proved to be uniformly better than the least squares estimator, that is, minimax in terms of risk under the Strawderman's loss function. Through simulation and empirical studies, they are also shown to be useful in the multicollinearity cases.     

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.     

基于奇异值分解的岭型回归(英文)

本文基于设计阵的奇异值分解(SVD),从LS估计出发,应用岭回归估计方法,构造了回归系数的一个新的有偏估计,称为基于SVD的岭型回归估计,简称RRSVD估计,讨论了其性质和偏参数的选取问题,得到了许多重要结论.计算结果表明,在设计阵呈病态时,RRS善岭回归估计.     

Inequality constrained ridge regression estimator

We carry out the idea of inequality constrained least squares (ICLS) estimation of Liew (1976) to the inequality constrained ridge regression (ICRR) estimation. We propose ICRR estimator by reducing the primal–dual relation to the fundamental problem of Dantzig and Cottle, 1967, Cottle and Dantzig, 1974 with Lemke (1962) algorithm. Furthermore, we conduct a Monte Carlo experiment.     

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。     

半参数可加模型的广义Liu估计

作为部分线性模型和可加模型的推广,半参数可加模型在统计建模中应用广泛.考虑这类半参数模型在线性部分自变量存在共线性时的估计问题.基于Profile最小二乘方法,提出了参数分量的广义Profile-Liu估计,并给出了该估计量的偏和方差以及均方误差.最后利用数值模拟验证了所提方法的有效性.     

追加数据对条件指数的影响<英>

克服线性回归模型中设计矩阵的复共线性,主要有三种方法:追加数据,自变量选择和非最小二乘法,本文研究追加数据在减少条件数中的作用,我们的研究表明,在可能情况下适当地选择追加数据,设计矩阵的条件指数可以被减少.我们用在回归最优设计中广泛被研究过的Gaylor-Merrill数据说明了本文理论结果的实用意义.     

A stochastic restricted ridge regression estimator

Groß [J. Groß, Restricted ridge estimation, Statistics & Probability Letters 65 (2003) 57–64] proposed a restricted ridge regression estimator when exact restrictions are assumed to hold. When there are stochastic linear restrictions on the parameter vector, we introduce a new estimator by combining ideas underlying the mixed and the ridge regression estimators under the assumption that the errors are not independent and identically distributed. Apart from [J. Groß, Restricted ridge estimation, Statistics & Probability Letters 65 (2003) 57–64], we call this new estimator as the stochastic restricted ridge regression (SRRR) estimator. The performance of the SRRR estimator over the mixed estimator in respect of the variance and the mean square error matrices is examined. We also illustrate our findings with a numerical example. The shrinkage generalized least squares (GLS) and the stochastic restricted shrinkage GLS estimators are proposed.