Adaptive SVD Soft-thresholding Estimators in Multivariate Regression

Details Adaptive SVD Soft-thresholding Estimators in Multivariate Regression Adaptive SVD Soft-thresholding Estimators in Multivariate Regression

2012-01-01

arxiv.org/abs/1201.0381v1

Statistics

Methodology

Scientific paper

The weighted nuclear-norm penalization is introduced, based on which we develop a new method for simultaneous dimension reduction and coefficient estimation in multivariate regression. Different from the classical reduced-rank regression where the coefficient matrix is estimated via hard-thresholding the singular value decomposition of the least-squares estimator of the data matrix, the proposed non-convex weighted nuclear-norm penalized method, leads to an adaptive soft-thresholding estimator (AST), which (i) is a global optimal solution of the proposed non-convex criterion, (ii) possesses better bias-variance property and (iii) enjoys low computational complexity. The rank consistency of the proposed AST estimator is shown for both classical and high-dimensional asymptotic regimes. The prediction and estimation performance bounds are also established. We contrast the AST estimator with the nuclear-norm penalized least-squares estimator (NNP) and the rank selection criterion (RSC). The efficacy of the AST estimator is demonstrated by extensive simulation studies and an application in genetics.

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