On estimation in the reduced-rank regression with a large number of responses and predictors

JOURNAL OF MULTIVARIATE ANALYSIS

卷:140

Article

Kargin, Vladislav

关键词: Random matrices;    High-dimensional data;    Reduced-rank regression;    Rank selection;    Rank estimation;    Tracy-Widom distribution;    Factor model;   

DOI  :  10.1016/j.jmva.2015.06.004

来源: Elsevier

【 摘 要 】

We consider a multivariate linear response regression in which the number of responses and predictors is large and comparable with the number of observations, and the rank of the matrix of regression coefficients is assumed to be small. We study the distribution of singular values for the matrix of regression coefficients and for the matrix of predicted responses. For both matrices, it is found that the limit distribution of the largest singular value is a rescaling of the Tracy-Widom distribution. Based on this result, we suggest algorithms for the model rank selection and compare them with the algorithm suggested by Bunea, She and Wegkamp. Next, we design two consistent estimators for the singular values of the coefficient matrix, compare them, and derive the asymptotic distribution for one of these estimators. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free