A new class of efficient and debiased two-step shrinkage estimators : method and application
(2022) In Journal of Applied Statistics 49(16). p.4181-4205- Abstract
This paper introduces a new class of efficient and debiased two-step shrinkage estimators for a linear regression model in the presence of multicollinearity. We derive the proposed estimators’ mean square error and define the necessary and sufficient conditions for superiority over the existing estimators. In addition, we develop an algorithm for selecting the shrinkage parameters for the proposed estimators. The comparison of the new estimators versus the traditional ordinary least squares, ridge regression, Liu, and the two-parameter estimators is done by a matrix mean square error criterion. The Monte Carlo simulation results show the superiority of the proposed estimators under certain conditions. In the presence of high but... (More)
This paper introduces a new class of efficient and debiased two-step shrinkage estimators for a linear regression model in the presence of multicollinearity. We derive the proposed estimators’ mean square error and define the necessary and sufficient conditions for superiority over the existing estimators. In addition, we develop an algorithm for selecting the shrinkage parameters for the proposed estimators. The comparison of the new estimators versus the traditional ordinary least squares, ridge regression, Liu, and the two-parameter estimators is done by a matrix mean square error criterion. The Monte Carlo simulation results show the superiority of the proposed estimators under certain conditions. In the presence of high but imperfect multicollinearity, the two-step shrinkage estimators’ performance is relatively better. Finally, two real-world chemical data are analyzed to demonstrate the advantages and the empirical relevance of our newly proposed estimators. It is shown that the standard errors and the estimated mean square error decrease substantially for the proposed estimator. Hence, the precision of the estimated parameters is increased, which of course is one of the main objectives of the practitioners.
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- author
- Qasim, Muhammad LU ; Månsson, Kristofer ; Sjölander, Pär and Kibria, B. M.Golam
- publishing date
- 2022
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- chemical structures, Debiased estimator, Monte Carlo simulations, multicollinearity, ridge regression, two-parameter estimator
- in
- Journal of Applied Statistics
- volume
- 49
- issue
- 16
- pages
- 25 pages
- publisher
- Routledge
- external identifiers
-
- scopus:85114876661
- ISSN
- 0266-4763
- DOI
- 10.1080/02664763.2021.1973389
- language
- English
- LU publication?
- no
- additional info
- Publisher Copyright: © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
- id
- 9f006fc8-f84c-4953-9026-ba1c300f537b
- date added to LUP
- 2025-03-24 17:21:23
- date last changed
- 2025-04-04 14:36:15
@article{9f006fc8-f84c-4953-9026-ba1c300f537b,
abstract = {{<p>This paper introduces a new class of efficient and debiased two-step shrinkage estimators for a linear regression model in the presence of multicollinearity. We derive the proposed estimators’ mean square error and define the necessary and sufficient conditions for superiority over the existing estimators. In addition, we develop an algorithm for selecting the shrinkage parameters for the proposed estimators. The comparison of the new estimators versus the traditional ordinary least squares, ridge regression, Liu, and the two-parameter estimators is done by a matrix mean square error criterion. The Monte Carlo simulation results show the superiority of the proposed estimators under certain conditions. In the presence of high but imperfect multicollinearity, the two-step shrinkage estimators’ performance is relatively better. Finally, two real-world chemical data are analyzed to demonstrate the advantages and the empirical relevance of our newly proposed estimators. It is shown that the standard errors and the estimated mean square error decrease substantially for the proposed estimator. Hence, the precision of the estimated parameters is increased, which of course is one of the main objectives of the practitioners.</p>}},
author = {{Qasim, Muhammad and Månsson, Kristofer and Sjölander, Pär and Kibria, B. M.Golam}},
issn = {{0266-4763}},
keywords = {{chemical structures; Debiased estimator; Monte Carlo simulations; multicollinearity; ridge regression; two-parameter estimator}},
language = {{eng}},
number = {{16}},
pages = {{4181--4205}},
publisher = {{Routledge}},
series = {{Journal of Applied Statistics}},
title = {{A new class of efficient and debiased two-step shrinkage estimators : method and application}},
url = {{http://dx.doi.org/10.1080/02664763.2021.1973389}},
doi = {{10.1080/02664763.2021.1973389}},
volume = {{49}},
year = {{2022}},
}