On singular value distribution of large dimensional data matrices whose columns have different correlations

2018/02/05 by Yin, Yanqing
#FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1802.01245

Abstract

Suppose \mathbf Y_n=(\mathbf y₁,⋯,\mathbf y_n) is a p× n data matrix whose columns \mathbf y_j, 1≤ j≤ n have different correlations. The asymptotic spectral property of \mathbf S_n=\frac1n\mathbf Y_n\mathbf Y^*_n when p increase with n has been considered by some authors recently. This model has known an increasing popularity due to its widely applications in multi-user multiple-input single-output (MISO) systems and robust signal processing. In this paper, for more convenient applications in practice, we will investigate the spectral distribution of \mathbf S_n under milder moment conditions than existing work. We also discuss a potential application in sample classification.

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