Variable selection by lasso-type methods

Abstract

Variable selection is an important property of shrinkage methods. The adaptive lasso is an oracle procedure and can do consistent variable selection. In this paper, we provide an explanation that how use of adaptive weights makes it possible for the adaptive lasso to satisfy the necessary and almost sufficient condition for consistent variable selection. We suggest a novel algorithm and give an important result that for the adaptive lasso normalisation of predictors after the introduction of adaptive weights makes the adaptive lasso performance identical to the lasso.