On a model selection problem from high-dimensional sample covariance matrices

• Published in: Journal of multivariate analysis Vol. 102; no. 10; pp. 1388 - 1398
• Main Authors: Chen, J., Delyon, B., Yao, J.-F.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 01.11.2011; Elsevier; Taylor & Francis LLC
• Series: Journal of Multivariate Analysis
• Subjects: Algebra; Cross-validation; Exact sciences and technology; High-dimensional data; Large sample covariance matrices; Linear and multilinear algebra, matrix theory; Marčenko–Pastur distribution; Mathematics; Matrix; Multivariate analysis; Order selection; Order selection Cross-validation Large sample covariance matrices High-dimensional data Marcenko-Pastur distribution; Parametric inference; Population; Probability and statistics; Probability distribution; Random variables; Sampling theory, sample surveys; Sciences and techniques of general use; Statistics; Statistics Theory; Studies; Variance analysis; secondary; High-dimensional data; Large sample covariance matrices; Order selection; Cross-validation; Marčenko–Pastur distribution; primary; Rank statistic; Random matrix; primary 62H25; Sample size; Large sample; Cross validation; Matrix theory; Multivariate analysis; secondary 60F05; Parametric method; 62E20; Distribution function; Selection method; Marcenko-Pastur distribution; Sample survey; Discriminant analysis; Model selection; Covariance matrix; Statistical method; Selection problem; 15A52; Sampling theory; Spectral distribution; Population size; Marčenko-Pastur distribution
• ISSN: 0047-259X; 1095-7243
• DOI: 10.1016/j.jmva.2011.05.005

Modern random matrix theory indicates that when the population size p is not negligible with respect to the sample size n , the sample covariance matrices demonstrate significant deviations from the population covariance matrices. In order to recover the characteristics of the population covariance matrices from the observed sample covariance matrices, several recent solutions are proposed when the order of the underlying population spectral distribution is known. In this paper, we deal with the underlying order selection problem and propose a solution based on the cross-validation principle. We prove the consistency of the proposed procedure.