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Recursive kernel estimator in a semiparametric regression model

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  • Emmanuel De Dieu Nkou

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.

Suggested Citation

  • Emmanuel De Dieu Nkou, 2023. "Recursive kernel estimator in a semiparametric regression model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 35(1), pages 145-171, January.
    • Handle: RePEc:taf:gnstxx:v:35:y:2023:i:1:p:145-171
    DOI: 10.1080/10485252.2022.2130308
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