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

Tatsuya Kubokawa and Muni S. Srivastava

Journal of Multivariate Analysis, 2008, vol. 99, issue 9, 1906-1928

Abstract: 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.

Keywords: primary; 62C20; 62H12 secondary; 62C12; 62H30 Covariance matrix Discriminant analysis Dominance property Efron-Morris loss function Empirical Bayes procedure Multivariate classification Precision matrix Singular Wishart Stein-Haff identity (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (18)

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