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.
Publié le : 1992-12-14
Classification:
Multivariate normal distribution,
covariance matrix,
hierachical prior,
inverted Wishart prior,
matrix exponential,
intraclass hypothesis,
Bayesian marginalization,
generalized linear model,
exchangeable distribution for a positive definite matrix,
62F15,
62C12,
62E20,
62E25,
62F11,
62G05,
62J10,
62J12
@article{1176348885,
author = {Leonard, Tom and Hsu, John S. J.},
title = {Bayesian Inference for a Covariance Matrix},
journal = {Ann. Statist.},
volume = {20},
number = {1},
year = {1992},
pages = { 1669-1696},
language = {en},
url = {http://dml.mathdoc.fr/item/1176348885}
}
Leonard, Tom; Hsu, John S. J. Bayesian Inference for a Covariance Matrix. Ann. Statist., Tome 20 (1992) no. 1, pp. 1669-1696. http://gdmltest.u-ga.fr/item/1176348885/