AISM 53, 691-707

© 2001 ISM

## Strong universal pointwise consistency of recursive regression estimates

### Harro Walk

Mathematisches Institut A, Universität Stuttgart,
Pfaffenwaldring 57, D-70569 Stuttgart, Germany

(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.

**Source**
(TeX , DVI )