Asymptotic distribution of the LR statistic for equality of the smallest eigenvalues in high-dimensional principal component analysis

Yasunori Fujikoshi, Takayuki Yamada, Daisuke Watanabe and Takakazu Sugiyama

Journal of Multivariate Analysis, 2007, vol. 98, issue 10, 2002-2008

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[set membership, variant](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 (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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