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 Wp−1(n,Σp−1) with large dimension p - 1, when Σp−1 = Ip−1. In this paper, we study the distribution of the second-largest latent root of the covariance matrix when Σp = 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.
International Journal of Knowledge Engineering and Soft Data Paradigms, 2013 Vol.4 No.2, pp.187 - 197
Available online: 08 Dec 2013 *Full-text access for editors Access for subscribers Purchase this article Comment on this article