Relaxed Adaptive Lasso and Its Asymptotic Results

Abstract

This article introduces a novel two-stage variable selection method to solve the common asymmetry problem between the response variable and its influencing factors. In practical applications, we cannot correctly extract important factors from a large amount of complex and redundant data. However, the proposed method based on the relaxed lasso and the adaptive lasso, namely, the relaxed adaptive lasso, can achieve information symmetry because the variables it selects contain all the important information about the response variables. The goal of this paper is to preserve the relaxed lasso’s superior variable selection speed while imposing varying penalties on different coefficients. Additionally, the proposed method enjoys favorable asymptotic properties, that is, consistency with a fast rate of convergence with Opn−1. The simulation demonstrates that the proper variable recovery, i.e., the number of significant variables selected, and prediction accuracy of the relaxed adaptive lasso in a limited sample is superior to the regular lasso, relaxed lasso and adaptive lasso estimators.