Variable Selection and Shrinkage Estimation in Linear Models Under Quadratic Risk

• Activity Number: 87
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Mohamed Amezziane* and S. Ejaz Ahmed
• Companies: Central Michigan University and Brock University
• Keywords: shrinkage estimation ; variable selection ; shrinkage coefficients ; linear model ; quadratic loss

Abstract

The proposed estimator is obtained by independently shrinking the parameters of some classical regression estimator towards zero. The mean square error of the estimator is minimized with respect to the shrinkage coefficients to simultaneously select relevant variables and estimate their associated regression coefficients. This results in a soft threshold estimator similar to the non-negative garrote, but does not employ a regularization parameter. The asymptotic properties of the estimator are derived and its performance is compared to that of penalized regression estimators through Monte Carlo simulation experiments.