Recursive kernel estimator in a semiparametric regression model. Issue 1 (2nd January 2023)

• Record Type: Journal Article
• Authors: Nkou, Emmanuel De Dieu
• Is Part Of: Journal of nonparametric statistics. Volume 35:Issue 1(2023)
• Page Start: 145
• Page End: 171
• Publication Date: 2023-01-02
• Subjects: Dimension reduction -- recursive kernel estimators -- asymptotic normality -- semiparametric regression -- sliced inverse regression; 62E20 -- 62F12 -- 62G05 -- 62J02; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2022.2130308
• Languages: English
• ISSNs: 1048-5252

Abstract

Abstract : 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.