Double shrunken selection operator

ABSTRACT

The least absolute shrinkage and selection operator (LASSO) is a prominent estimator which selects significant (under some sense) features and kills insignificant ones. Indeed the LASSO shrinks features larger than a noise level to zero. In this article, we force LASSO to be shrunken more by proposing a Stein-type shrinkage estimator emanating from the LASSO, namely the Stein-type LASSO. The newly proposed estimator proposes good performance in risk sense numerically. Variants of this estimator have smaller relative MSE and prediction error, compared to the LASSO, in the analysis of prostate cancer dataset.

KEYWORDS:

• Double shrinking
• LASSO
• Linear regression model
• MSE
• Prediction error
• Stein-type shrinkage estimator

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08
• 62J07
• 62G20

Acknowledgments

We would like to thank two anonymous referees for their valuable and constructive comments which significantly improved the presentation of the article and led to put many details.