Nonparametric Kernel Estimation For Functional Stationary Ergodic Data With Responses Missing At Random Or Randomly Censored

In this paper, we investigate the asymptotic properties of a non-parametric kermel estimation given a functional explanatory variable when functional stationary ergodic data and missing at random or randomly censored responses are observed. In addition, the finite-sample performances of the estimator are completed by simulations, which show the good behaviour of the estimator. The details are given as follows:On the one hand, we establish asymptotic properties for a conditional density estimator from which we derive almost sure convergence (with rate) and asymptotic normality of a conditional mode estimator. This new estimate take into account missing data and functional stationary ergodic data. Moreover, the asymptotic (1-α) confidence interval of the estimator are presented. Finally, a simulation study for different missing rates are performed to illustrate how this fact allows to get higher predictive performances than those obtained with standard estimates.On the other hand, we investigate the asymptotic properties of the kernel estimator for nonparametric regression operator when the functional stationary ergodic data with randomly censorship is considered. More precisely, we introduce the kernel type estimator of the nonparametric regression operator with the responses randomly censored, and establish the almost surely convergence with rate, as well as the asymptotic normality of the estimator. As an application of the asymptotic normality, the asymptotic (1-(?) confidence interval of the regression operator is also presented. Finally, the finite-sample performances of the estimator are completed by simulations, in which we calculate the average mean square error for different censored rates and histogram as well as Q-Q plot, which show the good behaviour of the estimator.