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On efficiency of some restricted estimators in a multivariate regression model

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  • Sévérien Nkurunziza

    (University of Windsor)

Abstract

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.

Suggested Citation

  • Sévérien Nkurunziza, 2023. "On efficiency of some restricted estimators in a multivariate regression model," Statistical Papers, Springer, vol. 64(2), pages 617-642, April.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:2:d:10.1007_s00362-022-01324-w
    DOI: 10.1007/s00362-022-01324-w
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    References listed on IDEAS

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    1. Fuqi Chen & Sévérien Nkurunziza, 2016. "A class of Stein-rules in multivariate regression model with structural changes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 83-102, March.
    2. Jain, Kanchan & Singh, Sukhbir & Sharma, Suresh, 2011. "Restricted estimation in multivariate measurement error regression model," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 264-280, February.
    3. Fuqi Chen & Sévérien Nkurunziza, 2017. "On estimation of the change points in multivariate regression models with structural changes," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(14), pages 7157-7173, July.
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