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Entropy loss and risk of improved estimators for the generalized variance and precision

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Abstract

Let the distributions of X(p×r) and S(p×p) be N(ζ, Σ⊗I r) and W p(n, Σ) respectively and let them be independent. The risk of the improved estimator for |Σ| or {ei329-1} based on X and S under entropy loss (=d/|Σ| −log(d/|Σ|)−1 or d|Σ|−log(d|Σ|)−1) is evaluated in terms of incomplete beta function of matrix argument and its derivative. Numerical comparison for the reduction of risk over the best affine equivariant estimator is given.

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Authors and Affiliations

  1. Department of Mathematics, University of Tsukuba, 305, Tsukuba, Ibaraki, Japan

    Nariaki Sugiura & Yoshihiko Konno

Authors
  1. Nariaki Sugiura
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  2. Yoshihiko Konno
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Dedicated to Professor Yukihiro Kodama on his 60th birthday.

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Sugiura, N., Konno, Y. Entropy loss and risk of improved estimators for the generalized variance and precision. Ann Inst Stat Math 40, 329–341 (1988). https://doi.org/10.1007/BF00052348

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  • DOI: https://doi.org/10.1007/BF00052348

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