Computation of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix

Nobuki Takayama; Lin Jiu; Satoshi Kuriki; Yi Zhang

doi:10.1016/j.jmva.2020.104642

Computation of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix

Nobuki Takayama
, Lin Jiu
, Satoshi Kuriki
, Yi Zhang^*

^*Corresponding author for this work

Department of Applied Mathematics

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

1 Citation (Scopus)

Abstract

We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for general dimension. The formula is expressed in terms of a definite integral with parameters. We derive a differential equation satisfied by the integral for the 2×2 matrix case and perform a numerical analysis of it.

Original language	English
Article number	104642
Journal	Journal of Multivariate Analysis
Volume	179
DOIs	https://doi.org/10.1016/j.jmva.2020.104642
Publication status	Published - Sept 2020

Keywords

Euler characteristic method
Holonomic gradient method
Real non-central Wishart distributions

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10.1016/j.jmva.2020.104642

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@article{3d50780c4b4e4937a3bc59426ac4cfe4,

title = "Computation of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix",

abstract = "We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for general dimension. The formula is expressed in terms of a definite integral with parameters. We derive a differential equation satisfied by the integral for the 2×2 matrix case and perform a numerical analysis of it.",

keywords = "Euler characteristic method, Holonomic gradient method, Real non-central Wishart distributions",

author = "Nobuki Takayama and Lin Jiu and Satoshi Kuriki and Yi Zhang",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2020",

month = sep,

doi = "10.1016/j.jmva.2020.104642",

language = "English",

volume = "179",

journal = "Journal of Multivariate Analysis",

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T1 - Computation of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix

AU - Takayama, Nobuki

AU - Jiu, Lin

AU - Kuriki, Satoshi

AU - Zhang, Yi

PY - 2020/9

Y1 - 2020/9

N2 - We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for general dimension. The formula is expressed in terms of a definite integral with parameters. We derive a differential equation satisfied by the integral for the 2×2 matrix case and perform a numerical analysis of it.

AB - We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for general dimension. The formula is expressed in terms of a definite integral with parameters. We derive a differential equation satisfied by the integral for the 2×2 matrix case and perform a numerical analysis of it.

KW - Euler characteristic method

KW - Holonomic gradient method

KW - Real non-central Wishart distributions

UR - https://www.scopus.com/pages/publications/85086478527

U2 - 10.1016/j.jmva.2020.104642

DO - 10.1016/j.jmva.2020.104642

M3 - Article

AN - SCOPUS:85086478527

SN - 0047-259X

VL - 179

JO - Journal of Multivariate Analysis

JF - Journal of Multivariate Analysis

M1 - 104642

ER -

Computation of the expected Euler characteristic for the largest eigenvalue of a real non-central Wishart matrix

Abstract

Keywords

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