Geodesic
Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study
Kybernetika, Tome 54 (2018) no. 5, pp. 958-977.

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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.
DOI : 10.14736/kyb-2018-5-0958
Classification : 62G05, 62J05, 62J07
Keywords: efficiency of LASSO; penalty estimators; preliminary test; Stein-type estimator; ridge estimator; L$_2$-risk function 
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     title = {Rank theory approach to ridge, {LASSO,} preliminary test and {Stein-type} estimators: {Comparative} study},
     journal = {Kybernetika},
     pages = {958--977},
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Saleh, A. K. Md. Ehsanes; Navrátil, Radim. Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study. Kybernetika, Tome 54 (2018) no. 5, pp. 958-977. doi : 10.14736/kyb-2018-5-0958. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2018-5-0958/

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