Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: comparative study

Title:

Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: comparative study

Creator:

Saleh, A. K. Md. Ehsanes and Navrátil, Radim

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7c531f96-420d-4725-ba37-ca9b5de079a2
uuid:7c531f96-420d-4725-ba37-ca9b5de079a2
doi:10.14736/kyb-2018-5-0958

Subject:

efficiency of LASSO, penalty estimators, preliminary test, Stein-type estimator, ridge estimator, and L2-risk function

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Source:

Kybernetika | 2018 Volume:54 | Number:5

Harvested from:

CDK

Metadata only:

false