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

J 2018

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

SALEH, A.K.Md.Ehsanes a Radim NAVRÁTIL

Základní údaje

Originální název

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

Autoři

SALEH, A.K.Md.Ehsanes a Radim NAVRÁTIL

Vydání

KYBERNETIKA, AV ČR, Institute of Information Theory and Automation of the Academy, 2018, 0023-5954

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10100 1.1 Mathematics

Stát vydavatele

Česká republika

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 0.560

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/18:00110994

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

efficiency of LASSO; penalty estimators; preliminary test; Stein-type estimator; ridge estimator; L-2-risk function

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 11. 5. 2020 16:49, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

MUNI/A/1204/2017, interní kód MU

Název: Matematické statistické modelování 2 (Akronym: MaStaMo2)

Investor: Masarykova univerzita, Matematické statistické modelování 2, DO R. 2020_Kategorie A - Specifický výzkum - Studentské výzkumné projekty

Citovat

SALEH, A.K.Md.Ehsanes a 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, roč. 54, č. 5, s. 958-977. ISSN 0023-5954. Dostupné z: https://doi.org/10.14736/kyb-2018-5-0958.

@article{1570677,
   author = {Saleh, A.K.Md.Ehsanes and Navrátil, Radim},
   article_number = {5},
   doi = {https://doi.org/10.14736/kyb-2018-5-0958},
   keywords = {efficiency of LASSO; penalty estimators; preliminary test; Stein-type estimator; ridge estimator; L-2-risk function},
   language = {eng},
   issn = {0023-5954},
   journal = {KYBERNETIKA},
   title = {Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study},
   url = {https://www.kybernetika.cz/content/2018/5/958},
   volume = {54},
   year = {2018}
}

TY  - JOUR
ID  - 1570677
AU  - Saleh, A.K.Md.Ehsanes - Navrátil, Radim
PY  - 2018
TI  - Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study
JF  - KYBERNETIKA
VL  - 54
IS  - 5
SP  - 958-977
EP  - 958-977
PB  - AV ČR, Institute of Information Theory and Automation of the Academy
SN  - 00235954
KW  - efficiency of LASSO
KW  - penalty estimators
KW  - preliminary test
KW  - Stein-type estimator
KW  - ridge estimator
KW  - L-2-risk function
UR  - https://www.kybernetika.cz/content/2018/5/958
L2  - https://www.kybernetika.cz/content/2018/5/958
N2  - 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.
ER  -

SALEH, A.K.Md.Ehsanes a Radim NAVRÁTIL. Rank theory approach to ridge, LASSO, preliminary test and Stein-type estimators: Comparative study. \textit{KYBERNETIKA}. AV ČR, Institute of Information Theory and Automation of the Academy, 2018, roč.~54, č.~5, s.~958-977. ISSN~0023-5954. Dostupné z: https://doi.org/10.14736/kyb-2018-5-0958.

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