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

Computation of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Non-central Wishart Matrix

Statistics Theory 2020-05-25 v2 Symbolic Computation Statistics Theory

Authors: Nobuki Takayama , Lin Jiu , Satoshi Kuriki , Yi Zhang

Abstract

We give an approximate formula for the distribution of the largest eigenvalue of real Wishart matrices by the expected Euler characteristic method for the 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 $2 \times 2$ matrix case and perform a numerical analysis of it.

Keywords

wishart matrix largest eigenvalue expected euler characteristic definite integral differential equation numerical analysis

Cite

@article{arxiv.1903.10099,
  title  = {Computation of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Non-central Wishart Matrix},
  author = {Nobuki Takayama and Lin Jiu and Satoshi Kuriki and Yi Zhang},
  journal= {arXiv preprint arXiv:1903.10099},
  year   = {2020}
}

Computation of the Expected Euler Characteristic for the Largest Eigenvalue of a Real Non-central Wishart Matrix

Abstract

Keywords

Cite

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