Envelope-based sparse reduced-rank regression for multivariate linear model

Envelope models were first proposed by Cook et al. (2010) as a method to reduce estimative and predictive variations in multivariate regression. Sparse reduced-rank regression, introduced by Chen and Huang (2012), is a widely used technique that performs dimension reduction and variable selection simultaneously in multivariate regression. In this work, we combine envelope models and sparse reduced-rank regression method to propose an envelope-based sparse reduced-rank regression estimator, and then establish its consistency, asymptotic normality and oracle property in highdimensional data. We carry out some Monte Carlo simulation studies and also analyze two datasets to demonstrate that the proposed envelope-based sparse reduced-rank regression method displays good variable selection and prediction performance.