Publication details
Rank Theory Approach to Ridge, LASSO,Preliminary Test and Stein-type Estimators: A Comparative Study
| Authors | |
|---|---|
| Year of publication | 2018 |
| Type | Article in Periodical |
| Magazine / Source | The Canadian Journal of Statistics |
| MU Faculty or unit | |
| Citation | |
| Web | http://dx.doi.org/10.1002/cjs.11480 |
| 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 |
| Attached files | |
| Description | 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. |