On the UMVU estimator for the generalized variance of the multinomial family

Abdelaziz Ghribi

Communications in Statistics - Theory and Methods, 2019, vol. 48, issue 24, 5943-5952

Abstract: The generalized variance is an important statistical indicator which appears in a number of statistical topics. It is a successful measure for multivariate data concentration. In this article, we established, in a closed form, the bias of the generalized variance maximum likelihood estimator of the Multinomial family. We also derived, with a complete proof, the uniformly minimum variance unbiased estimator (UMVU) for the generalized variance of this family. These results rely on explicit calculations, the completeness of the exponential family and the Lehmann–Scheffé theorem.

Date: 2019
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DOI: 10.1080/03610926.2018.1520888

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