On the distribution of the second-largest latent root for certain high dimensional Wishart matrices
by Takayuki Iimori; Toru Ogura; Takakazu Sugiyama
International Journal of Knowledge Engineering and Soft Data Paradigms (IJKESDP), Vol. 4, No. 2, 2013

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.

Online publication date: Sun, 08-Dec-2013

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