AISM 53, 691-707
© 2001 ISM
(Received January 7, 1999; revised February 28, 2000)
Abstract. For semi-recursive and recursive kernel estimates of a regression of $Y$ on $X$ ($d$-dimensional random vector $X$, integrable real random variable $Y$), introduced by Devroye and Wagner and by Révész, respectively, strong universal pointwise consistency is shown, i.e. strong consistency $P_{X}$-almost everywhere for general distribution of $(X,Y)$. Similar results are shown for the corresponding partitioning estimates.
Key words and phrases: Nonparametric regression estimation, semi-recursive estimation, recursive estimation, kernel estimates, partitioning estimates, strong universal pointwise consistency, strong laws of large numbers, conditional expectations, truncation, covering.