BAYESIAN-INFERENCE FOR A COVARIANCE-MATRIX

• 成果类型: Article
• 署名作者: LEONARD, T; HSU, JSJ
• 署名单位: University of California System; University of California Santa Barbara
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176348885
• 发表日期: 1992
• 页码: 1669-1696
• 关键词: Empirical Bayes; linear-model

摘要

A flexible class of prior distributions is proposed, for the covariance matrix of a multivariate normal distribution, yielding much more general hierarchical and empirical Bayes smoothing and inference, when compared with a conjugate analysis involving an inverted Wishart distribution. A likelihood approximation is obtained for the matrix logarithm of the covariance matrix, via Bellman's iterative solution to a Volterra integral equation. Exact and approximate Bayesian, empirical and hierarchical Bayesian estimation and finite sample inference techniques are developed. Some risk and asymptotic frequency properties are investigated. A subset of the Project Talent American High School data is analyzed. Applications and extensions to multivariate analysis, including a generalized linear model for covariance matrices, are indicated.