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 ofa given regression model, we find that the RR estimator dominates the LSE, RE, PTE, Stein-type estimators and LASSO estimator uniformly, while, similar to [17], neither LASSO nor LSE, PTE and Stein-Typeestimators dominates the other. Our conclusions are based on the analysis of L2-risks and relative risk efficiencies (RRE) together with the RRE related tables and graphs.

Additional Metadata
Keywords Dominance, Efficiency, LASSO, Penalty estimator, Pre-test and Stein-type estimators, Risk function
Persistent URL dx.doi.org/10.19139/soic-2310-5070-713
Journal Statistics, Optimization and Information Computing
Citation
Saleh, A.K.Md.E, Golam Kibria, B.M. (B. M.), & George, F. (Florence). (2019). Comparative study of LASSO, ridge regression, preliminary test and stein-type estimators for the sparse gaussian regression model. Statistics, Optimization and Information Computing, 7(4), 626–641. doi:10.19139/soic-2310-5070-713