In the development of efficient predictive models, the key is to identify suitable predictors for a given linear model. For the first time, this paper provides a comparative study of ridge regression, LASSO, preliminary test and Stein-type estimators based on the theory of rank statistics. Under the orthonormal design matrix of a given linear model, we find that the rank based ridge estimator outperforms the usual rank estimator, restricted R-estimator, rank-based LASSO, preliminary test and Stein-type R-estimators uniformly. On the other hand, neither LASSO nor the usual R-estimator, preliminary test and Stein-type R-estimators outperform the other. The region of domination of LASSO over all the R-estimators (except the ridge R-estimator) is the interval around the origin of the parameter space. Finally, we observe that the L2-risk of the restricted R-estimator equals the lower bound on the L2-risk of LASSO. Our conclusions are based on L2-risk analysis and relative L2-risk efficiencies with related tables and graphs.

Additional Metadata
Keywords Efficiency of LASSO, L2-risk function, Penalty estimators, Preliminary test, Ridge estimator, Stein-type estimator
Persistent URL dx.doi.org/10.14736/kyb-2018-5-0958
Journal Kybernetika
Citation
Saleh, A.K.Md.E, & Navrátil, R. (Radim). (2018). Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study. Kybernetika, 54(5), 958–977. doi:10.14736/kyb-2018-5-0958