Nonparametric regression estimation for functional stationary ergodic data with missing at random

In this paper, we investigate the asymptotic properties of the estimator for the regression function operator whenever the functional stationary ergodic data with missing at random (MAR) are considered. Concretely, we construct the kernel type estimator of the regression operator for functional stationary ergodic data with the responses MAR, and some asymptotic properties such as the convergence rate in probability as well as the asymptotic normality of the estimator are obtained under some mild conditions respectively. As an application, the asymptotic (1-zeta) confidence interval of the regression operator is also presented for 0 < zeta< 1. Finally, a simulation study is carried out to compare the finite sample performance based on mean square error between the classical functional regression in complete case and the functional regression with MAR. (C) 2015 Elsevier B.V. All rights reserved.