Minimax Estimation of a Multivariate Normal Mean with Unknown Covariance Matrix.
PURDUE UNIV LAFAYETTE IND DEPT OF STATISTICS
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Let X be a p-variate por3 vector, normally distributed with unknown mean theta and unknown covariance matrix sigma. Let WpXp be distributed independently of X, and let W have a Wishart distribution with n degrees of freedom and parameter sigma. It is desired to estimate theta under the quadratic loss delta-thetaQdelta-theta, where Q is a known positive definite matrix. Under the condition that a lower bound for the smallest characteristic root of Q sigma is known, a family of minimax estimators is developed.
- Statistics and Probability