ON RANDOM-DESIGN MODEL WITH DEPENDENT ERRORS
Jan Mielniczuk, Wei Biao Wu · 2004
We consider random-design nonparametric regression model in which errors depend on predictors as well as on unobservable latent variables. Predic- tors 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 de- pendence structure.