Nonparametric regression estimation under mixing conditions

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.