A high-dimensional test for the equality of the smallest eigenvalues of a covariance matrix

By James R. Schott. 2006

68 citations recorded by the source corpus.

For the test of sphericity, Ledoit and Wolf [Ann. Statist. 30 (2002) 1081-1102] proposed a statistic which is robust against high dimensionality. In this paper, we consider a natural generalization of their statistic for the test that the smallest eigenvalues of a covariance matrix are equal. Some inequalities are obtained for sums of eigenvalues and sums of squared eigenvalues. These bounds permit us to obtain the asymptotic null distribution of our statistic, as the dimensionality and sample size go to infinity together, by using distributional results obtained by Ledoit and Wolf [Ann. Statist. 30 (2002) 1081-1102]. Some empirical results comparing our test with the likelihood ratio test are also given.

Subfields: Applied Mathematics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/869a6f17d57aa060f7a3e66764d0d9ca46b5586c

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In Applied Mathematics

In Statistics and Probability

Citations in the corpus

Consistency of AIC and BIC in estimating the number of significant components in high-dimensional principal component analysis (2018, background): “The asymptotic framework that the largest k population eigenvalues tending to infinity was introduced in Schott (2006), and in Fujikoshi et al. (2007).”
Asymptotic power of sphericity tests for high-dimensional data (2013, background): “48 67 v1 [ m at h. ST ] 2 0 Ju n 20 13 The Annals of Statistics 2013, Vol. 41, No. 3, 1204–1231 DOI: 10.1214/13-AOS1100 c© Institute of Mathematical Statistics, 2013”
Determining the number of components in a factor model from limited noisy data (2008, background): “In [30,32] it is proved that in the asymptotic limit”
Non-Parametric Detection of the Number of Signals: Hypothesis Testing and Random Matrix Theory (2009, methodology): “7 shows simulation results for the probability of misdetection as a function of signal strength for our algorithm with %, the algorithm proposed by Rao and Edelman [30], and the algorithm by Schott [32], with a confidence level of %, for and real valued observations .”