Computational Statistics & Data Analysis
Some high-dimensional tests for a one-way MANOVA
Journal of Multivariate Analysis
Non-parametric detection of the number of signals: hypothesis testing and random matrix theory
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
A new test for sphericity of the covariance matrix for high dimensional data
Journal of Multivariate Analysis
International Journal of Knowledge Engineering and Soft Data Paradigms
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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.