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, least absolute shrinkage and selector operator (LASSO), preliminary test (PTE) 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, PTE 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 L2-risk of the restricted R-estimator equals the lower bound on the L2-risk of LASSO. Our conclusions are based on L2-risk analysis and relative L2-risk efficiencies with related tables and graphs. The Canadian Journal of Statistics 46: 690–704; 2018

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Keywords Efficiency of LASSO, L2-risk function, Penalty estimators, Preliminary test and Stein-type estimator, Rank estimators
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Journal Canadian Journal of Statistics
Saleh, A.K.Md.E, Navrátil, R. (Radim), & Norouzirad, M. (Mina). (2018). Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: A comparative study. Canadian Journal of Statistics, 46(4), 690–704. doi:10.1002/cjs.11480