Estimation under the matrix variate elliptical model

Janet  van Niekerk; Andriette Bekker; Mohammad Arashi; Daan J. de Waal

doi:10.37920/sasj.2016.50.1.7

Janet van Niekerk Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria, South Africa
Andriette Bekker Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria, South Africa
Mohammad Arashi Department of Statistics, School of Mathematical Sciences, University of Shahrood, Shahrood, Iran; Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria, South Africa
Daan J. de Waal Department of Mathematical Statistics and Actuarial Science, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein, South Africa; Department of Statistics, Faculty of Natural and Agricultural Sciences, University of Pretoria, Pretoria, South Africa

DOI: https://doi.org/10.37920/sasj.2016.50.1.7

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

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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