Recursive kernel estimator in a semiparametric regression model

• Published in: Journal of nonparametric statistics Vol. 35; no. 1; pp. 145 - 171
• Main Author: Nkou, Emmanuel De Dieu
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 02.01.2023; Taylor & Francis Ltd
• Subjects: Algorithms; Approximation; asymptotic normality; Dimension reduction; Identification methods; Kernels; Normality; Performance evaluation; Recursive algorithms; recursive kernel estimators; Recursive methods; Regression analysis; Regression models; semiparametric regression; sliced inverse regression
• ISSN: 1048-5252; 1029-0311; 1026-7654; 1029-0311
• DOI: 10.1080/10485252.2022.2130308

Sliced inverse regression (SIR) is a recommended method to identify and estimate the central dimension reduction (CDR) subspace. CDR subspace is at the base to describe the conditional distribution of the response Y given a d-dimensional predictor vector X. To estimate this space, two versions are very popular: the slice version and the kernel version. A recursive method of the slice version has already been the subject of a systematic study. In this paper, we propose to study the kernel version. It's a recursive method based on a stochastic approximation algorithm of the kernel version. The asymptotic normality of the proposed estimator is also proved. A simulation study that not only shows the good numerical performance of the proposed estimate and which also allows to evaluate its performance with respect to existing methods is presented. A real dataset is also used to illustrate the approach.