Journal of the Japanese Society of Computational Statistics
Online ISSN : 1881-1337
Print ISSN : 0915-2350
ISSN-L : 0915-2350
Theory and Applications
DISTRIBUTION OF THE LARGEST EIGENVALUE OF AN ELLIPTICAL WISHART MATRIX AND ITS SIMULATION
Aya ShinozakiHiroki HashiguchiToshiya Iwashita
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2018 Volume 30 Issue 2 Pages 1-12

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Abstract

This paper provides an alternative proof of the derivation of the distribution of the largest eigenvalue of an elliptical Wishart matrix in contrast to the result of CaroLopera et al. (2016). We show the relation between multivariate and matrix-variate t distributions. From this relation, we can generate random numbers drawn from the matrix-variate t distribution. A Monte Carlo simulation is conducted to evaluate the accuracy for the truncated distribution function of the largest eigenvalue of the elliptical Wishart matrix. Exact computation of the distribution of the smallest eigenvalue is also presented.

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