We consider an infinite sequence X1,X2,... of independent random variables having a common continuous distribution function F(x). For 1[less-than-or-equals, slant]i[less-than-or-equals, slant]n, let {Xi:n} denote the ith order statistic among X1,...,Xn. In this paper, we characterize the...

Let (X, Y) be an d--valued regression pair, whereXhas a density andYis bounded. Ifni.i.d. samples are drawn from this distribution, the Nadaraya-Watson kernel regression estimate in dwith Hilbert kernelK(x)=1/||x||dis shown to converge weakly for all such regression pairs. We also show that...

Consider the d-dimensional unit cube [0,1]d and portion it into n regions, A1,..., An. Select and fix a point in each one of these regions so we have x1,..., xn. Consider observable variables Yi, i = 1,..., n, satisfying the multivariate regression model Yi = g(xi) + [var epsilon]i, where g is...