Strong Consistency And Additive Model Of Internal Kernel Estimation

In this paper, we mainly investigate the problem of nonparametric regression. We investigate two parts of results. In the first part, the strong consistency of the multivariate internal nonparametric estimator is investigated under strong mix-ing dependence assumption. This estimator is particularly easy to use when we model the regression function by additive nonparametric structure. The point-wise strong consistency and its rate are given as well as that over a compact set, under suitable conditions. In the second part, we investigate the asymptotic normality of an estimator of nonparametric additive model under strong mixing dependence assumption by integration method using the internal estimator.