Estimation of the Precision Matrix of a Singular Wishart Distribution and its Application in High Dimensional Data
AbstractIn this article, 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 the use of the ridge-type empirical Bayes estimators provides higher correct classication rates.
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Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-362.
Length: 26 pages
Date of creation: Aug 2005
Date of revision:
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