On the asymptotic behavior of the Nadaraya-Watson estimator associated with the recursive SIR method

Bernard Bercu 1, 2 Thi Mong Ngoc Nguyen 1, 3 Jérôme Saracco 1, 3
2 ALEA - Advanced Learning Evolutionary Algorithms
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
3 CQFD - Quality control and dynamic reliability
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We investigate the asymptotic behavior of the 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 estimator. We also illustrate our semiparametric estimation procedure on simulated data.
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Bernard Bercu, Thi Mong Ngoc Nguyen, Jérôme Saracco. On the asymptotic behavior of the Nadaraya-Watson estimator associated with the recursive SIR method. Statistics, Taylor & Francis: STM, Behavioural Science and Public Health Titles, 2014, pp.17. ⟨hal-00673832⟩

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