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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 make it possible for the adaptive lasso to satisfy the necessary and almost sufcient condition for consistent variable selection. We suggest a novel algorithm and give an important result that for the adaptive lasso if predictors are normalised after the introduction of adaptive weights, it makes the adaptive lasso performance identical to the lasso.

Keywords

Lasso Adaptive lasso Variable selection LARS

Article Details

Author Biographies

Sohail Chand, College of Statistical and Actuarial Sciences University of the Punjab Quaid-i-Azam Campus Lahore Pakistan

Assistant Professor

Shahid Kamal, College of Statistical and Actuarial Sciences University of the Punjab Quaid-i-Azam Campus Lahore Pakistan

Professor