Recursive kernel estimator in a semiparametric regression model

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.

Keywords:

• Dimension reduction
• recursive kernel estimators
• asymptotic normality
• semiparametric regression
• sliced inverse regression

Mathematics Subject Classification 2020:

• 62E20
• 62F12
• 62G05
• 62J02

Acknowledgements

The author also thanks Dr. Stéphane Bouka for the fruitful discussions which made it possible to carry out this work. The author would like to thank the Editor and the two referees for their very helpful comments, which led to a considerable improvement of the original version of the paper and a more sharply focused presentation.

Disclosure statement

No potential conflict of interest was reported by the author.