Abstract: We consider random-design nonparametric regression model in which errors depend on predictors as well as on unobservable latent variables. Predictors and latent variables may be short- or long-range dependent. In this setup asymptotic distributions of the Nadaraya-Watson estimate of regression function are studied under various conditions. We prove that their form depends on three factors: amount of smoothing and strength of dependence of both predictors and latent variables. Our results go beyond earlier ones by allowing more general dependence structure.
Key words and phrases: Kernel regression estimators, linear process, long- and short-range dependence, martingale Central Limit Theorem, random-design regression.