CONSISTENT NONPARAMETRIC MULTIPLE-REGRESSION FOR DEPENDENT HETEROGENEOUS PROCESSES - THE FIXED DESIGN CASE

Consider the nonparametric regression model Yi(n) = g(xi(n)) + εi(n), i = 1, ..., n, where g is an unknown regression function and assumed to be bounded and real valued on A ⊂ Rp, xi(n)'s are known and fixed design points and εi(n)'s are assumed to be both dependent and non-identically distributed random variables. This paper investigates the asymptotic properties of the general nonparametric regression estimator gn(x) = Σi = 1n Wni(x) Yi(n), where the weight function Wni(x) is of the form Wni(x) = Wni(x; x1(n), x2(n), ..., xn(n). The estimator gn(x) is shown to be weak, mean square error, and universal consistent under very general conditions on the temporal dependence and heterogeneity of εi(n)'s. Asymptotic distribution of the estimator is also considered. © 1990.