Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study

Warning

This publication doesn't include Faculty of Sports Studies. It includes Faculty of Science. Official publication website can be found on muni.cz.
Authors

SALEH A.K.Md.Ehsanes NAVRÁTIL Radim

Year of publication 2018
Type Article in Periodical
Magazine / Source KYBERNETIKA
MU Faculty or unit

Faculty of Science

Citation
Web https://www.kybernetika.cz/content/2018/5/958
Doi http://dx.doi.org/10.14736/kyb-2018-5-0958
Keywords efficiency of LASSO; penalty estimators; preliminary test; Stein-type estimator; ridge estimator; L-2-risk function
Description 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 L-2-risk of the restricted R-estimator equals the lower bound on the L-2-risk of LASSO. Our conclusions are based on L-2-risk analysis and relative L-2-risk efficiencies with related tables and graphs.
Related projects:

You are running an old browser version. We recommend updating your browser to its latest version.

More info