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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F18%3A00110994" target="_blank" >RIV/00216224:14310/18:00110994 - isvavai.cz</a>

Výsledek na webu

<a href="https://www.kybernetika.cz/content/2018/5/958" target="_blank" >https://www.kybernetika.cz/content/2018/5/958</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.14736/kyb-2018-5-0958" target="_blank" >10.14736/kyb-2018-5-0958</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10100 - Mathematics

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

KYBERNETIKA

ISSN

0023-5954

e-ISSN

—

Svazek periodika

54

Číslo periodika v rámci svazku

5

Stát vydavatele periodika

CZ - Česká republika

Počet stran výsledku

20

Strana od-do

958-977

Kód UT WoS článku

000455560300006

EID výsledku v databázi Scopus

2-s2.0-85064205850