A new class of generalized Bayes minimax ridge regression estimators

• 成果类型: Article
• 署名作者: Maruyama, Y; Strawderman, WE
• 署名单位: University of Tokyo; Rutgers University System; Rutgers University New Brunswick
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/009053605000000327
• 发表日期: 2005
• 页码: 1753-1770
• 关键词: multivariate normal distribution; matrix

摘要

Let y = A beta + epsilon, where y is an N x 1 vector of observations, beta is a p x I vector of unknown regression coefficients, A is an N x p design matrix and E is a spherically symmetric error term with unknown scale parameter a. We consider estimation of under general quadratic loss functions, and, in particular, extend the work of Strawderman [J. Amer Statist. Assoc. 73 (1978) 623-627] and Casella [Ann. Statist. 8 (1980) 1036-1056, J. Amer. Statist. Assoc. 80 (1985) 753-758] by finding adaptive minimax estimators (which are, under the nonnality assumption, also generalized Bayes) of beta, which have greater numerical stability (i.e., smaller condition number) than the usual least squares estimator. In particular, we give a subclass of such estimators which, surprisingly, has a very simple form. We also show that under certain conditions the generalized Bayes minimax estimators in the normal case are also generalized Bayes and minimax in the general case of spherically symmetric errors.