Asymptotic properties of adaptive group Lasso for sparse reduced rank regression. Issue 1 (18th October 2016)

• Record Type: Journal Article
• Authors: He, Kejun; Huang, Jianhua Z.
• Is Part Of: Stat. Volume 5:Issue 1(2016)
• Page Start: 251
• Page End: 261
• Publication Date: 2016-10-18
• Subjects: high dimensional regression -- large sample theory -- minimax -- multivariate regression -- oracle property -- variable selection; Statistics -- Periodicals; 519.2
• DOI: 10.1002/sta4.123
• Languages: English
• ISSNs: 2049-1573

Abstract

Abstract : This paper studies the asymptotic properties of the penalized least squares estimator using an adaptive group Lasso penalty for the reduced rank regression. The group Lasso penalty is defined in the way that the regression coefficients corresponding to each predictor are treated as one group. It is shown that under certain regularity conditions, the estimator can achieve the minimax optimal rate of convergence. Moreover, the variable selection consistency can also be achieved, that is, the relevant predictors can be identified with probability approaching one. In the asymptotic theory, the number of response variables, the number of predictors and the rank number are allowed to grow to infinity with the sample size. Copyright © 2016 John Wiley & Sons, Ltd.