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Decision Theoretic Estimation of the Ratio of Variances in a Bivariate Normal Distribution

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Abstract

In this paper the problem of estimating the ratio of variances, σ, in a bivariate normal distribution with unknown mean is considered from a decision-theoretic point of view. First, the UMVU estimator of σ is derived, and then it is shown to be inadmissible under two specific loss functions, namely, the squared error loss and the entropy loss. The derivation of the results is done by conditioning on an auxiliary negative binomial random variable.

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Authors and Affiliations

  1. Department of Mathematics, University of Patras, 26500 Rio, Patras, Greece

    George Iliopoulos

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  1. George Iliopoulos
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Iliopoulos, G. Decision Theoretic Estimation of the Ratio of Variances in a Bivariate Normal Distribution. Annals of the Institute of Statistical Mathematics 53, 436–446 (2001). https://doi.org/10.1023/A:1014600625165

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