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Strong consistency of kernel estimator in a semiparametric regression model
Statistics ( IF 1.2 ) Pub Date : 2019-08-26 , DOI: 10.1080/02331888.2019.1656723
Emmanuel de Dieu Nkou 1 , Guy Martial Nkiet 1
Affiliation  

ABSTRACT Estimating the effective dimension reduction (EDR) space, related to the semiparametric regression model introduced by Li [Sliced inverse regression for dimension reduction. J Amer Statist Assoc. 1991;86:316–327], is based on the estimation of the covariance matrix Λ of the conditional expectation of the vector of predictors given the response. An estimator of Λ based on kernel method was introduced by Zhu and Fang [Asymptotics for kernel estimate of sliced inverse regression. Ann Statist. 1996;24:1053–1068] who then derived, under some conditions, the asymptotic distribution of , as . In this paper, we obtain the almost sure convergence of to Λ, as .

中文翻译:

半参数回归模型中核估计量的强一致性

摘要 估计有效降维 (EDR) 空间,与 Li 引入的半参数回归模型相关 [用于降维的切片逆回归。J Amer Statist Assoc。1991;86:316-327],基于对给定响应的预测变量向量的条件期望的协方差矩阵 Λ 的估计。Zhu和Fang介绍了一种基于核方法的Λ估计量[Asymptotics for kernel估计的切片逆回归。安统计员。1996;24:1053-1068] 然后他在某些条件下推导出 的渐近分布,如 。在本文中,我们获得了对 Λ 的几乎肯定的收敛性,如 。
更新日期:2019-08-26
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