Consistent nonparametric multiple regression for dependent heterogeneous processes: The fixed design case

Y. Fan

Journal of Multivariate Analysis, 1990, vol. 33, issue 1, 72-88

Abstract: Consider the nonparametric regression model Yi(n) = g(xi(n)) + [var epsilon]i(n), i = 1, ..., n, where g is an unknown regression function and assumed to be bounded and real valued on A [subset of] Rp, xi(n)'s are known and fixed design points and [var epsilon]i(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) = [Sigma]i = 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 [var epsilon]i(n)'s. Asymptotic distribution of the estimator is also considered.

Keywords: nonparametric; estimation; regression; function; mixingale; near; epoch; dependent; mixing; sequence; martingale; difference; sequence; consistency; multivariate; central; limit; theorem (search for similar items in EconPapers)
Date: 1990
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Citations: View citations in EconPapers (20)

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