On the asymptotic behaviour of the recursive Nadaraya–Watson estimator associated with the recursive sliced inverse regression method |
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Authors: | Bernard Bercu Thi Mong Ngoc Nguyen |
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Institution: | 1. Université de Bordeaux, Institut de Mathématiques de Bordeaux, UMR CNRS 5251, 351 cours de la libération, 33405 Talence cedex, France;2. Université de Strasbourg, Institut de Recherche Mathématique Avancée, UMR CNRS 7501, 7 rue René Descartes 67084 Strasbourg cedex, France |
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Abstract: | We investigate the asymptotic behaviour of the recursive Nadaraya–Watson estimator for the estimation of the regression function in a semiparametric regression model. On the one hand, we make use of the recursive version of the sliced inverse regression method for the estimation of the unknown parameter of the model. On the other hand, we implement a recursive Nadaraya–Watson procedure for the estimation of the regression function which takes into account the previous estimation of the parameter of the semiparametric regression model. We establish the almost sure convergence as well as the asymptotic normality for our Nadaraya–Watson estimate. We also illustrate our semiparametric estimation procedure on simulated data. |
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Keywords: | semi-parametric regression recursive estimation Nadaraya–Watson estimator sliced inversion regression |
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