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On efficiency of some restricted estimators in a multivariate regression model
Statistical Papers ( IF 1.3 ) Pub Date : 2022-06-18 , DOI: 10.1007/s00362-022-01324-w
Sévérien Nkurunziza

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.



中文翻译:

关于多元回归模型中一些受限估计量的效率

在本文中,我们研究了多元测量误差回归模型中的约束估计问题。特别是,我们推导了回归系数矩阵的无限制估计量(UE)和受限估计量(REs)的联合渐近正态性。导出的结果在假设的限制下以及在替代限制的序列下成立。此外,我们为 UE 和 RE 建立了渐近分布风险,并比较了它们的相对性能。确定在限制附近,受限估计器 (RE) 比 UE 执行得更好。但是当远离限制时,RE 的性能比 UE 差。此外,我们通过模拟探索收缩估计器(SE)的性能。数值结果证实了关于 RE 和 UE 之间的相对风险优势的既定理论结果。研究结果还表明,在限制附近,RE 主导 SE,但当远离限制时,RE 表现不佳,而 SE 始终主导 UE。

更新日期:2022-06-19
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