A new class of efficient and debiased two-step shrinkage estimators: method and application.

Content Provider	Europe PMC
Author	Qasim, Muhammad Månsson, Kristofer Sjölander, Pär Kibria, B. M. Golam
Copyright Year	2021
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 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.
Related Links	https://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC9639496&blobtype=pdf
Page Count	25
ISSN	02664763
Volume Number	49
DOI	10.1080/02664763.2021.1973389
PubMed Central reference number	PMC9639496
Issue Number	16
PubMed reference number	36353298
Journal	Journal of Applied Statistics [J Appl Stat]
e-ISSN	13600532
Language	English
Publisher	Taylor & Francis
Publisher Date	2021-09-14
Access Restriction	Open
Rights License	This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. © 2021 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group
Subject Keyword	Debiased estimator Monte Carlo simulations multicollinearity two-parameter estimator ridge regression chemical structures
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Statistics, Probability and Uncertainty