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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10103 - Statistics and probability

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2018

Kód důvěrnosti údajů

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

Název periodika

The Canadian Journal of Statistics

ISSN

0319-5724

e-ISSN

1708-945X

Svazek periodika

46

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

CA - Kanada

Počet stran výsledku

15

Strana od-do

690-704

Kód UT WoS článku

000454597800009

EID výsledku v databázi Scopus

2-s2.0-85059551935