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@article{1452016,
author = {Saleh, A.K.Md.Ehsanes and Navrátil, Radim and Norouzirad, Mina},
article_number = {4},
doi = {http://dx.doi.org/10.1002/cjs.11480},
keywords = {Efficiency of LASSO; Penalty estimators; Rank estimators; Preliminary test and Stein-type estimator; L_2-risk function},
language = {eng},
issn = {0319-5724},
journal = {The Canadian Journal of Statistics},
title = {Rank Theory Approach to Ridge, LASSO,Preliminary Test and Stein-type Estimators: A Comparative Study},
url = {http://dx.doi.org/10.1002/cjs.11480},
volume = {46},
year = {2018}
}
TY - JOUR
ID - 1452016
AU - Saleh, A.K.Md.Ehsanes - Navrátil, Radim - Norouzirad, Mina
PY - 2018
TI - Rank Theory Approach to Ridge, LASSO,Preliminary Test and Stein-type Estimators: A Comparative Study
JF - The Canadian Journal of Statistics
VL - 46
IS - 4
SP - 690-704
EP - 690-704
PB - Wiley
SN - 03195724
KW - Efficiency of LASSO
KW - Penalty estimators
KW - Rank estimators
KW - Preliminary test and Stein-type estimator
KW - L_2-risk function
UR - http://dx.doi.org/10.1002/cjs.11480
N2 - In the development of efficient predictive models, the key is to identify suitable predictors to establish a prediction model for a given linear or nonlinear model. 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 dominance of LASSO over all the R-estimators (except the ridge R-estimator) is the sparsity-dimensional interval around the origin of the parameter space. 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.
ER -
SALEH, A.K.Md.Ehsanes, Radim NAVRÁTIL and Mina NOROUZIRAD. Rank Theory Approach to Ridge, LASSO,Preliminary Test and Stein-type Estimators: A Comparative Study. \textit{The Canadian Journal of Statistics}. Wiley, 2018, vol.~46, No~4, p.~690-704. ISSN~0319-5724. Available from: https://dx.doi.org/10.1002/cjs.11480.
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