Approximation of upper percentile points for the second largest latent root in principal component analysis. (1st January 2013)

• Record Type: Journal Article
• Authors: Sugiyama, Takakazu; Ogura, Toru; Takeda, Yuichi; Hashiguchi, Hiroki
• Is Part Of: International journal of knowledge engineering and soft data paradigms. Volume 4:Number 2(2013)
• Page Start: 107
• Page End: 117
• Publication Date: 2013-01-01
• Subjects: approximate distribution -- principal component analysis -- second largest latent root -- upper percentile point -- wishart matrix; Soft computing -- Periodicals; Statistics -- Periodicals; Information science -- Periodicals; 003.05
• Languages: English
• ISSNs: 1755-3210

Abstract

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.