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

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  • Fan, Y.
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    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.

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    Bibliographic Info

    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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    Related research

    Keywords: nonparametric estimation regression function mixingale near epoch dependent mixing sequence martingale difference sequence consistency multivariate central limit theorem;

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    Cited by:
    1. Liang, Han-Ying & Jing, Bing-Yi, 2005. "Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 227-245, August.
    2. Kapetanios, George, 2007. "Estimating deterministically time-varying variances in regression models," Economics Letters, Elsevier, vol. 97(2), pages 97-104, November.
    3. Zhou, Xing-cai & Lin, Jin-guan, 2012. "A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error’s structure," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1914-1922.
    4. Yang, Shanchao, 2003. "Uniformly asymptotic normality of the regression weighted estimator for negatively associated samples," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 101-110, April.

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