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 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.

Online publication date: Sat, 19-Jul-2014

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