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

Listed author(s):
  • Fan, Y.
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    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.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 33 (1990)
    Issue (Month): 1 (April)
    Pages: 72-88

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    Handle: RePEc:eee:jmvana:v:33:y:1990:i:1:p:72-88
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