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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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