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

SALEH, A.K.Md.Ehsanes and Radim NAVRÁTIL. Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study. KYBERNETIKA. AV ČR, Institute of Information Theory and Automation of the Academy, 2018, vol. 54, No 5, p. 958-977. ISSN 0023-5954. Available from: https://dx.doi.org/10.14736/kyb-2018-5-0958.

Basic information

• Original name: Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study
• Authors: SALEH, A.K.Md.Ehsanes (124 Canada) and Radim NAVRÁTIL (203 Czech Republic, guarantor, belonging to the institution).
• Edition: KYBERNETIKA, AV ČR, Institute of Information Theory and Automation of the Academy, 2018, 0023-5954.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10100 1.1 Mathematics
• Country of publisher: Czech Republic
• Confidentiality degree: is not subject to a state or trade secret
• WWW: URL
• Impact factor: Impact factor: 0.560
• RIV identification code: RIV/00216224:14310/18:00110994
• Organization unit: Faculty of Science
• Doi: http://dx.doi.org/10.14736/kyb-2018-5-0958
• UT WoS: 000455560300006
• Keywords in English: efficiency of LASSO; penalty estimators; preliminary test; Stein-type estimator; ridge estimator; L-2-risk function
• Tags: rivok
• Tags: International impact, Reviewed

Abstract

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 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.

Links

• MUNI/A/1204/2017, interní kód MU: Name: Matematické statistické modelování 2 (Acronym: MaStaMo2)

Investor: Masaryk University, Category A