Rank Theory Approach to Ridge, LASSO,Preliminary Test and Stein-type Estimators: A Comparative Study

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F18%3A00104101" target="_blank" >RIV/00216224:14310/18:00104101 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1002/cjs.11480" target="_blank" >http://dx.doi.org/10.1002/cjs.11480</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1002/cjs.11480" target="_blank" >10.1002/cjs.11480</a>

Result language

angličtina

Original language name

Rank Theory Approach to Ridge, LASSO,Preliminary Test and Stein-type Estimators: A Comparative Study

Original language 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.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10103 - Statistics and probability

Project

—

Continuities

S - Specificky vyzkum na vysokych skolach

Publication year

2018

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

The Canadian Journal of Statistics

ISSN

0319-5724

e-ISSN

1708-945X

Volume of the periodical

46

Issue of the periodical within the volume

4

Country of publishing house

CA - CANADA

Number of pages

15

Pages from-to

690-704

UT code for WoS article

000454597800009

EID of the result in the Scopus database

2-s2.0-85059551935