Estimation of the precision matrix of a singular Wishart distribution and its application in high-dimensional data

JOURNAL OF MULTIVARIATE ANALYSIS

卷:99

Article

Kubokawa, Tatsuya¹  Srivastava, Muni S.² 

[1] Univ Tokyo, Fac Econ, Bunkyo Ku, Tokyo 1130033, Japan

[2] Univ Toronto, Dept Stat, Toronto, ON M5S 3G3, Canada

关键词: Covariance matrix;    Discriminant analysis;    Dominance property;    Efron-Morris loss function;    Empirical Bayes procedure;    Multivariate classification;    Precision matrix;    Singular Wishart;    Stein-Haff identity;   

DOI  :  10.1016/j.jmva.2008.01.016

来源: Elsevier

【 摘 要 】

In this article, the Stein-Haff identity is established for a singular Wishart distribution with a positive definite mean matrix but with the dimension larger than the degrees of freedom. This identity is then used to obtain estimators of the precision matrix improving on the estimator based on the Moore-Penrose inverse of the Wishart matrix under the Efron-Morris loss function and its variants. Ridge-type empirical Bayes estimators of the precision matrix are also given and their dominance properties over the usual one are shown using this identity. Finally, these precision estimators are used in a quadratic discriminant rule, and it is shown through simulation that discriminant methods based on the ridge-type empirical Bayes estimators provide higher correct classification rates. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

Free