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Nonparametric regression estimation under mixing conditions

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  • Roussas, George G.

Abstract

For j=1, 2,..., let {Zj}={(Xj, Yj)} be a strictly stationary sequence of random variables, where the X's and the Y's are 1p-valued and 1q-valued, respectively, for some integers p, q[greater-or-equal, slanted]1. Let [phi] be an integrable Borel real-valued function defined on 1q and set 97. The function [phi] need not be bounded. The quantity r(x) is estimated by 22, where fn(x) is a kernel estimate for the probability density function f of the X's and Rn(x)=(nhp)-1[Sigma]nj=1[phi](Yj) · K((x-Xj)/h). If the sequence {Zj} enjoys any one of the standard four kinds of mixing properties, then, under suitable additional assumptions, rn(x) is strongly consistent, uniformly over compacts. Rates of convergence are also specified.

Suggested Citation

  • Roussas, George G., 1990. "Nonparametric regression estimation under mixing conditions," Stochastic Processes and their Applications, Elsevier, vol. 36(1), pages 107-116, October.
    • Handle: RePEc:eee:spapps:v:36:y:1990:i:1:p:107-116
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