Title: On the distribution of the second-largest latent root for certain high dimensional Wishart matrices

Authors: Takayuki Iimori; Toru Ogura; Takakazu Sugiyama

Addresses: Kyorin Pharmaceutical Co., Ltd., 2-5, Kandasurugadai, Chiyoda-Ku, Tokyo, 101-0062, Japan ' Chuo University, 1-13-27, Kasuga, Bunkyo-Ku, Tokyo, 112-8551, Japan ' Soka University, 1-236, Tangi-Cho, Hachioji-Shi, Tokyo, 192-8577, Japan

Abstract: The distribution of the largest latent root was found by Johnstone (2001) for Wishart distributions W_p−1(n,Σ_p−1) with large dimension p - 1, when Σ_p−1 = I_p−1. In this paper, we study the distribution of the second-largest latent root of the covariance matrix when Σ_p = diag(σ, 1,..., 1) with σ » 1. When N = n - 1 and p are large and satisfy N/(p - 1) → γ* ≥ 1, we shall obtain the approximate distribution of the second-largest latent root, and verify the accuracy of the approximate distribution via a simulation study.

Keywords: intraclass correlation matrix; second-largest latent root; Wishart distribution; simulation.

DOI: 10.1504/IJKESDP.2013.058130

International Journal of Knowledge Engineering and Soft Data Paradigms, 2013 Vol.4 No.2, pp.187 - 197

Published online: 19 Jul 2014 *

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