Approximation of upper percentile points for the second largest latent root in principal component analysis

The approximate distribution of the largest latent root was proposed by Sugiyama 1972b. We extend his idea and propose an approximate distribution of the upper percentile points for the second largest latent root of the Wishart matrix. The proposed approximate distribution is adjusted by the expectation of each latent root. The simulation results show the validity of our adjustment for the expectation of each latent root, and the proposed approximate distribution is effective also in various cases, even when the dimension and sample size are both large.

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