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April 2012 A Robbins–Monro procedure for estimation in semiparametric regression models
Bernard Bercu, Philippe Fraysse
Ann. Statist. 40(2): 666-693 (April 2012). DOI: 10.1214/12-AOS969

Abstract

This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins–Monro procedure. On the one hand, we propose a stochastic algorithm similar to that of Robbins–Monro in order to estimate the shift parameter. A preliminary evaluation of the regression function is not necessary to estimate the shift parameter. On the other hand, we make use of a recursive Nadaraya–Watson estimator for the estimation of the regression function. This kernel estimator takes into account the previous estimation of the shift parameter. We establish the almost sure convergence for both Robbins–Monro and Nadaraya–Watson estimators. The asymptotic normality of our estimates is also provided. Finally, we illustrate our semiparametric estimation procedure on simulated and real data.

Citation

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Bernard Bercu. Philippe Fraysse. "A Robbins–Monro procedure for estimation in semiparametric regression models." Ann. Statist. 40 (2) 666 - 693, April 2012. https://doi.org/10.1214/12-AOS969

Information

Published: April 2012
First available in Project Euclid: 17 May 2012

zbMATH: 1273.62065
MathSciNet: MR2933662
Digital Object Identifier: 10.1214/12-AOS969

Subjects:
Primary: 62G05
Secondary: 62G20

Keywords: asymptotic properties , estimation of a regression function , estimation of a shift , Semiparametric estimation

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.40 • No. 2 • April 2012
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