Improved estimation in a multivariate regression with measurement error

• Published in: Journal of statistical computation and simulation Vol. 94; no. 8; pp. 1691 - 1714
• Main Authors: Nkurunziza, Sévérien, (Eric) Li, Yubin
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 23.05.2024; Taylor & Francis Ltd
• 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
• DOI: 10.1080/00949655.2023.2299346
• ISSN: 0094-9655

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.