Recursive kernel estimator in a semiparametric regression model

Emmanuel De Dieu Nkou

Journal of Nonparametric Statistics, 2023, vol. 35, issue 1, 145-171

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.

Date: 2023
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DOI: 10.1080/10485252.2022.2130308

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