Asymptotic distribution of the LR statistic for equality of the smallest eigenvalues in high-dimensional principal component analysis |
| |
Authors: | Yasunori Fujikoshi Takayuki Yamada Daisuke Watanabe Takakazu Sugiyama |
| |
Affiliation: | aDepartment of Mathematics, Graduate School of Science and Engineering, Chuo University, Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan |
| |
Abstract: | This paper deals with the distribution of the LR statistic for testing the hypothesis that the smallest eigenvalues of a covariance matrix are equal. We derive an asymptotic null distribution of the LR statistic when the dimension p and the sample size N approach infinity, while the ratio p/N converging on a finite nonzero limit c(0,1). Numerical simulations revealed that our approximation is more accurate than the classical chi-square-type approximation as p increases in value. |
| |
Keywords: | Asymptotic distribution High-dimensional principal component LR statistic Equality of the smallest eigenvalues |
本文献已被 ScienceDirect 等数据库收录! |