Algorithm for the product of Jack polynomials and its application to the sphericity test

Koki Shimizu; Hiroki Hashiguchi

doi:10.1016/j.spl.2022.109505

Algorithm for the product of Jack polynomials and its application to the sphericity test

Koki Shimizu, Hiroki Hashiguchi

Department of Applied Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We derive the distribution of a ratio of the largest and smallest eigenvalues of a singular beta-Wishart matrix. We propose an algorithm for calculating the product of Jack polynomials. Numerical computation for the derived distributions is performed using the algorithm.

Original language	English
Article number	109505
Journal	Statistics and Probability Letters
Volume	187
DOIs	https://doi.org/10.1016/j.spl.2022.109505
Publication status	Published - Aug 2022

Keywords

Elementary symmetric function
Jack polynomials
Singular Wishart distribution
Zonal polynomials

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10.1016/j.spl.2022.109505

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title = "Algorithm for the product of Jack polynomials and its application to the sphericity test",

abstract = "We derive the distribution of a ratio of the largest and smallest eigenvalues of a singular beta-Wishart matrix. We propose an algorithm for calculating the product of Jack polynomials. Numerical computation for the derived distributions is performed using the algorithm.",

keywords = "Elementary symmetric function, Jack polynomials, Singular Wishart distribution, Zonal polynomials",

author = "Koki Shimizu and Hiroki Hashiguchi",

note = "Funding Information: The authors wish to thank the referee and Editor-in-Chief for their helpful comments and suggestions. This research was supported by JSPS KAKENHI, Japan Grant Number 18K03428 . Publisher Copyright: {\textcopyright} 2022",

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doi = "10.1016/j.spl.2022.109505",

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AU - Shimizu, Koki

AU - Hashiguchi, Hiroki

N1 - Funding Information: The authors wish to thank the referee and Editor-in-Chief for their helpful comments and suggestions. This research was supported by JSPS KAKENHI, Japan Grant Number 18K03428 . Publisher Copyright: © 2022

PY - 2022/8

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N2 - We derive the distribution of a ratio of the largest and smallest eigenvalues of a singular beta-Wishart matrix. We propose an algorithm for calculating the product of Jack polynomials. Numerical computation for the derived distributions is performed using the algorithm.

AB - We derive the distribution of a ratio of the largest and smallest eigenvalues of a singular beta-Wishart matrix. We propose an algorithm for calculating the product of Jack polynomials. Numerical computation for the derived distributions is performed using the algorithm.

KW - Elementary symmetric function

KW - Jack polynomials

KW - Singular Wishart distribution

KW - Zonal polynomials

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U2 - 10.1016/j.spl.2022.109505

DO - 10.1016/j.spl.2022.109505

M3 - Article

AN - SCOPUS:85129842160

VL - 187

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

M1 - 109505

ER -

Algorithm for the product of Jack polynomials and its application to the sphericity test

Abstract

Keywords

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