Improved estimation in a multivariate regression with measurement error

In this paper, we study the estimation problem about the regression coefficients of a multivariate regression model with measurement errors under some uncertain restrictions. Specifically, we propose the unrestricted estimator (UE) and three restricted estimators (REs), and prove that they are all c...

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Bibliographic Details
Published in:Journal of statistical computation and simulation 2024-05, Vol.94 (8), p.1691-1714
Main Authors: Nkurunziza, Sévérien, (Eric) Li, Yubin
Format: Article
Language:English
Subjects:
ADR
asymptotic normality
Asymptotic properties
Constrictions
Error analysis
Estimators
measurement error
Multivariate analysis
multivariate regression model
Regression coefficients
Regression models
restricted estimator
shrinkage estimators
Stein rules
unrestricted estimator
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Summary:In this paper, we study the estimation problem about the regression coefficients of a multivariate regression model with measurement errors under some uncertain restrictions. Specifically, we propose the unrestricted estimator (UE) and three restricted estimators (REs), and prove that they are all consistent for the true coefficients. We derive the asymptotic distributions of the proposed estimators under the sequence of local alternative restrictions. We also propose shrinkage estimators (SEs) to address the problem of the uncertainty of the restrictions. In addition, we establish the asymptotic distributional risk (ADR) of the proposed estimators and compare the risk performance of these estimators. It is established that the REs perform better than the UE only near the restriction, while they perform poorly as one moves farther away from the restriction. We also prove that SEs dominate the UE. These theoretical results are confirmed by simulations.
ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2023.2299346