Central limit theorem for linear spectral statistics of large dimensional separable sample covariance matrices

2016/11/28 by Zhidong, Bai, Huiqin, Li, Guangming, Pan · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1611.08979

Abstract

Suppose that \mathbf X_n=(x_jk) is N× n whose elements are independent real variables with mean zero, variance 1 and the fourth moment equal to three. The separable sample covariance matrix is defined as B_n = \frac1NT_2n^1/2 X_n T_1n X_n' T_2n^1/2 where T_1n is a symmetric matrix and T_2n^1/2 is a symmetric square root of the nonnegative definite symmetric matrix T_2n. Its linear spectral statistics (LSS) are shown to have Gaussian limits when n/N approaches a positive constant.

Cited by

• Asymptotic distributions of four linear hypotheses test statistics under generalized spiked model
• LSD of sample covariances of superposition of matrices with separable covariance structure

Related

• Central limit theorem for linear spectral statistics of general separable sample covariance matrices with applications
• CLT for LSS of sample covariance matrices with unbounded dispersions
• CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data
• CLT for Linear Spectral Statistics in High-Dimensional Random Effects Models
• LSD of sample covariances of superposition of matrices with separable covariance structure