Comparative Study of LASSO, Ridge Regression, Preliminary Test and Stein-type Estimators for the Sparse Gaussian Regression Model

  • A K Md E Saleh Department of Mathematics and Statistics, Carleton University, Canada
  • B M Golam Kibria Department of Mathematics and Statistics, Florida International University, U.S.A
  • Florence Geroge Department of Mathematics and Statistics, Florida International University, U.S.A
Keywords: Dominance, Efficiency, LASSO, Penalty estimator, Pre-test and Stein-type estimators, Risk function

Abstract

This paper compares the performance characteristics of penalty estimators, namely, LASSO and ridge regression (RR), with the least squares estimator (LSE), restricted estimator (RE), preliminary test estimator (PTE) and the Stein-type estimators. Under the assumption of orthonormal design matrix of a given regression model, we find that the RR estimator dominates the LSE, RE, PTE, Stein-type estimators and LASSO estimator uniformly, while, similar to Hansen (2013), neither LASSO nor LSE, PTE and Stein-Type estimators dominates the other. Our conclusions are based on the analysis of L_2-risks and relative risk efficiencies (RRE) together with the RRE related tables and graphs.

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Published
2019-12-01
How to Cite
Saleh, A. K. M. E., Kibria, B. M. G., & Geroge, F. (2019). Comparative Study of LASSO, Ridge Regression, Preliminary Test and Stein-type Estimators for the Sparse Gaussian Regression Model. Statistics, Optimization & Information Computing, 7(4), 626-641. https://doi.org/10.19139/soic-2310-5070-713
Section
Research Articles