Asymptotic distribution of the LR statistic for equality of the smallest eigenvalues in high-dimensional principal component analysis
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.
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Volume (Year): 98 (2007)
Issue (Month): 10 (November)
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- Schott, James R., 2006. "A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 827-843, April.
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