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Estimation of the parameters of a Wishart extension on symmetric matrices

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Abstract

This paper deals with the parameters of a natural extension of the Wishart distribution, that is the Riesz distribution on the space of symmetric matrices. We estimate the shape parameter using two different approaches. The first one is based on the method of moments, we give its expression and investigate some of its properties. The second represents the maximum likelihood estimator. Unfortunately, in this case we do not have an explicit formula for this estimator. This latter is expressed in terms of the digamma function and sample mean of log-gamma variables. However, we derive the strong consistency and asymptotic normality properties of this estimator. A numerical comparative study between the two estimators is carried out in order to test the performance of the proposed approaches. For the second parameter, that is the scale parameter, we prove that the distribution of the maximum likelihood estimator given by Kammoun et al. (J Statist Prob Lett 126:127–131, 2017) is related to the Riesz distribution. We examine some properties concerning this estimator and we assess its performance by a numerical study.

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Acknowledgements

The authors would like to thank the Editor, Associate editor and referees for their carefully readings and for their suggestions and recommendations that have led to significant improvements in this paper.

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Authors and Affiliations

  1. ESPRIT School of Engineering, Z.I. Chotrana II, 2083, Tunis, Tunisia

    Emna Ghorbel

  2. Faculty of Sciences of Sfax, University of Sfax, 3038, Sfax, Tunisia

    Kaouthar Kammoun & Akram Sallem

  3. National School of Electronics and Telecommunications of Sfax, University of Sfax, 3018, Sfax, Tunisia

    Mahdi Louati

Authors
  1. Emna Ghorbel
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  2. Kaouthar Kammoun
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  3. Mahdi Louati
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  4. Akram Sallem
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Correspondence to Mahdi Louati.

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Ghorbel, E., Kammoun, K., Louati, M. et al. Estimation of the parameters of a Wishart extension on symmetric matrices. J. Korean Stat. Soc. 51, 1071–1089 (2022). https://doi.org/10.1007/s42952-022-00176-2

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  • DOI: https://doi.org/10.1007/s42952-022-00176-2

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