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

Saleh, A. K. Md. Ehsanes, and Navrátil, Radim. "Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study." Kybernetika 54.5 (2018): 958-977. <http://eudml.org/doc/294545>.

@article{Saleh2018,
abstract = {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.},
author = {Saleh, A. K. Md. Ehsanes, Navrátil, Radim},
journal = {Kybernetika},
keywords = {efficiency of LASSO; penalty estimators; preliminary test; Stein-type estimator; ridge estimator; L$_2$-risk function},
language = {eng},
number = {5},
pages = {958-977},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study},
url = {http://eudml.org/doc/294545},
volume = {54},
year = {2018},
}

TY - JOUR
AU - Saleh, A. K. Md. Ehsanes
AU - Navrátil, Radim
TI - Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study
JO - Kybernetika
PY - 2018
PB - Institute of Information Theory and Automation AS CR
VL - 54
IS - 5
SP - 958
EP - 977
AB - 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.
LA - eng
KW - efficiency of LASSO; penalty estimators; preliminary test; Stein-type estimator; ridge estimator; L$_2$-risk function
UR - http://eudml.org/doc/294545
ER -