## The Annals of Probability

### On Almost Sure Convergence of Conditional Empirical Distribution Functions

Winfried Stute

#### Abstract

We investigate the almost sure convergence of a kernel-type conditional empirical distribution function both in sup-norm and weighted sup-norms. As an application we get a strong law for the Nadaraya-Watson estimate of a regression function $m(\mathbf{x}) = \mathbb{E}(Y\mid \mathbf{X} = \mathbf{x})$ under a weak moment condition on $Y$.

#### Article information

Source
Ann. Probab., Volume 14, Number 3 (1986), 891-901.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176992445

Digital Object Identifier
doi:10.1214/aop/1176992445

Mathematical Reviews number (MathSciNet)
MR841591

Zentralblatt MATH identifier
0593.60043

JSTOR