Improvement of sphericity test for large-dimensional covariance matrix

A new test for sphericity of the covariance matrix for high dimensional data

AMS subject classifications: 62H10 62H15 Keywords: Covariance matrix Hypothesis testing High-dimensional data analysis a b s t r a c t 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 < trΣ the concentration, a new statistic is developed utilizing the rat...

On the sphericity test with large-dimensional observations

Testing Block Sphericity of a Covariance Matrix 27

This article deals with the problem of testing the hypothesis that q p-variate normal distributions are independent and that their covariance matrices are equal. The exact null distribution of the likelihood ratio statistic when q = 2 is obtained using inverse Mellin transform and the definition of Meijer’s G-function. Results for p = 2, 3, 4 and 5 are given in computable series forms.

Estimation of the Covariance Matrix of Large Dimensional Data

This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although such a regime is of interest for many current statistical signal processing and wireless communication issues, traditional methods fail to produce consistent es...

Corrections to LRT on Large Dimensional Covariance Matrix by RMT

Abstract: In this paper, we give an explanation to the failure of two likelihood ratio procedures for testing about covariance matrices from Gaussian populations when the dimension is large compared to the sample size. Next, using recent central limit theorems for linear spectral statistics of sample covariance matrices and of random F-matrices, we propose necessary corrections for these LR tes...