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

  • Authors:

  • Takayuki Iimori;Toru Ogura;Takakazu Sugiyama

  • Affiliations:

  • 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

  • Venue:
  • International Journal of Knowledge Engineering and Soft Data Paradigms
  • Year:
  • 2013

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Abstract

The distribution of the largest latent root was found by Johnstone 2001 for Wishart distributions Wp−1n,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 = diagσ, 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.