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：

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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 。