Estimation under the matrix variate elliptical model

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Van Niekerk, Janet
Bekker, Andriette, 1958-
Arashi, Mohammad
De Waal, Duan J.31cca2cb-0f0b-4ea7-a9c1-9711569804a7

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South African Statistical Association

Abstract

The problem of estimation within the matrix variate elliptical model is addressed. In this paper a subjective Bayesian approach is followed to derive new estimators for the parameters of the matrix variate elliptical model by assuming the previously intractable normal-Wishart prior. These new estimators are compared to the estimators derived under a normal-inverse Wishart prior as well as the objective Jeffreys’ prior which results in the maximum likelihood estimators, using different measures. A valuable contribution is the development of algorithms for the simulation of the posterior distributions of the matrix variate parameters with emphasis on the new proposed estimators. A simulation study as well as Fisher’s Iris data set are used to illustrate the novelty of these new estimators and to investigate the accuracy gained by assuming the normal-Wishart prior.

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Keywords

Bayesian inference, Bessel function of matrix argument, Characteristic matrix, Matrix variate elliptical model, Maximum posterior mode, Normal-inverse Wishart, Normal-Wishart, Squared error loss

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Van Niekerk, J, Bekker, A & Arashi, M 2016, 'Estimation under the matrix variate elliptical model', South African Statistical Journal, vol. 50, no. 1, pp. 189-171.