  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.
