Asymptotic normality of the Nadaraya–Watson estimator for nonstationary functional data and applications to telecommunications

Abstract

We study a nonparametric regression model, where the explanatory variable is nonstationary dependent functional data and the response variable is scalar. Assuming that the explanatory variable is a nonstationary mixture of stationary processes and general conditions of dependence of the observations (implied in particular by weak dependence), we obtain the asymptotic normality of the Nadaraya–Watson estimator. Under some additional regularity assumptions on the regression function, we obtain asymptotic confidence intervals for the regression function. We apply this result to estimate the quality of service for an end-to-end connection on a network.