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Ghorbel, Emna; Kammoun, Kaouthar; Louati, Mahdi; Sallem, Akram

Estimation of the parameters of a Wishart extension on symmetric matrices. (English) Zbl 1524.62255

J. Korean Stat. Soc. 51, No. 4, 1071-1089 (2022).
Summary: 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 K. Kammoun et al. [Stat. Probab. Lett. 126, 127–131 (2017; Zbl 1457.62064)] is related to the Riesz distribution. We examine some properties concerning this estimator and we assess its performance by a numerical study.

MSC:

62H12 Estimation in multivariate analysis
60B20 Random matrices (probabilistic aspects)

Keywords:

Cholesky decomposition; digamma function; maximum likelihood estimator; mean squared error; method of moments; Riesz distribution

Citations:

Zbl 1457.62064

Software:

DLMF
Cite Review PDF
Full Text: DOI

References:

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