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...

Let {(Xi, Yi)} be a stationary ergodic time series with (X, Y) values in the product space Rd[circle times operator]R. This study offers what is believed to be the first strongly consistent (with respect to pointwise, least-squares, and uniform distance) algorithm for inferring...

The strong universal pointwise consistency of some modified versions of the standard regression function estimates of partitioning, kernel, and nearest neighbor type is shown.

Let {Xj}j = - [infinity][infinity] be a vector-valued stationary process with a first-order univariate probability density f on Rd. We consider the recursive estimation of f(x) from n observations {Xj}j=1n which need not be independent. For processes {Xj}j = - [infinity][infinity] which are...

The almost sure convergence of the kernel-type density estimate is proved for a strictly stationary ergodic sample.