A new test for sphericity of the covariance matrix for high dimensional data
A new test for sphericity of the covariance matrix for high dimensional data
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DOI：
10.1016/j.jmva.2010.07.004
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发表时间：
2010-11-01
影响因子：
1.6
通讯作者：
Gallagher, Colin M.
中科院分区：
文献类型：
--
作者：
Fisher, Thomas J.;Sun, Xiaogian;Gallagher, Colin M.
本文提出了一种新的检验协方差矩阵球度的方法，当维数p超过样本量N = N + 1时。假设(A) 0 < tr σ (i)/p <∞，当i = 1时p ->∞，…， 16和(B) p/n -> c <∞称为浓度，利用样本协方差矩阵特征值的第四和第二次算术平均值的比率建立了一个新的统计量。新定义的检验具有许多理想的一般渐近性质，如(n, p) ->∞时的正态性和一致性。我们的模拟结果表明，新的测试与当前文献中的球度测试相当，在某些情况下甚至更强大。(c) 2010爱思唯尔公司版权所有。
In this paper we propose a new test procedure for sphericity of the covariance matrix when the dimensionality, p, exceeds that of the sample size, N = n + 1. Under the assumptions that (A) 0 < tr Sigma(i)/p < infinity as p -> infinity for i = 1,..., 16 and (B) p/n -> c < infinity known as the concentration, a new statistic is developed utilizing the ratio of the fourth and second arithmetic means of the eigenvalues of the sample covariance matrix. The newly defined test has many desirable general asymptotic properties, such as normality and consistency when (n, p) -> infinity. Our simulation results show that the new test is comparable to, and in some cases more powerful than, the tests for sphericity in the current literature. (c) 2010 Elsevier Inc. All rights reserved.