On efficiency of some restricted estimators in a multivariate regression model

• Published in: Statistical papers (Berlin, Germany) Germany), 2023-04, Vol.64 (2), p.617-642
• Main Author: Nkurunziza, Sévérien
• Format: Article
• Language: English
• Subjects: Asymptotic methods; Asymptotic properties; Chemical elements; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Efficiency; Error analysis; Estimators; Finance; Insurance; Management; Mathematics and Statistics; Multivariate analysis; Normality; Operations Research/Decision Theory; Probability Theory and Stochastic Processes; Regression coefficients; Regression models; Regular Article; Restrictions; Simulation; Statistics; Statistics for Business; Variables
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-022-01324-w

In this paper, we study a constrained estimation problem in a multivariate measurement error regression model. In particular, we derive the joint asymptotic normality of the unrestricted estimator (UE) and the restricted estimators (REs) of the matrix of the regression coefficients. The derived result holds under the hypothesized restriction as well as under the sequence of alternative restrictions. In addition, we establish Asymptotic Distributional Risk for the UE and the REs and compare their relative performance. It is established that near the restriction, the restricted estimators (REs) perform better than the UE. But the REs perform worse than the UE when one moves far away from the restriction. Further, we explore by simulation the performance of the shrinkage estimators (SEs). The numerical findings corroborate the established theoretical results about the relative risk dominance between the REs and the UE. The findings also show that near the restriction, the REs dominate SEs but as one moves far away from the restriction, REs perform poorly while SEs dominate always the UE.