Minimax estimators for a multinormal precision matrix

L. R. Haff

Journal of Multivariate Analysis, 1977, vol. 7, issue 3, 374-385

Abstract: Let Sp-p ~ Wishart ([Sigma], k), [Sigma] unknown, k > p + 1. Minimax estimators of [Sigma]-1 are given for L1, an Empirical Bayes loss function; and L2, a standard loss function (Ri [reverse not equivalent] E(Li | [Sigma]), I = 1, 2). The estimators are , a, b >= 0, r(·) a functional on Rp(p+2)/2. Stein, Efron, and Morris studied the special cases and , for certain, a, b. From their work , a = k - p - 1, b = p2 + p - 2; whereas, we prove . The reversal is surprising because a.e. (for a particular L2). Assume (compact) [subset of] , the set of p - p p.s.d. matrices. A "divergence theorem" on functions Fp-p : --> implies identities for Ri, i = 1, 2. Then, conditions are given for , i = 1, 2. Most of our results concern estimators with r(S) = t(U)/tr(S), U = p |S|1/p/tr(S).

Keywords: Precision; matrix; Stokes'; theorem; minimax; estimators; quadratic; loss (search for similar items in EconPapers)
Date: 1977
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Citations: View citations in EconPapers (12)

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