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

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

2012-02-24

arxiv.org/abs/1202.5432v1

Mathematics

Statistics Theory

Scientific paper

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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