Central limit theorem for quadratic errors of Nadaraya-Watson regression estimator under dependence

In this paper, we derive the central limit theorem (CLT) for quadratic error where the Nadaraya-Watson regression estimator is employed under dependence. Our results may be applicable for various nonparametric regression models including nonlinear auto-regressive model. In addition, we discuss the usefulness of our results for obtaining test statistics specifying a regression model under dependence. The proof uses CLT for variable degenerate U-statistics due to Kim and Luo (in press).