The Annals of Probability

On Almost Sure Convergence of Conditional Empirical Distribution Functions

Winfried Stute

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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

Permanent link to this document
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
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 62G05: Estimation 62J02: General nonlinear regression

Keywords
Conditional empirical distribution function Glivenko-Cantelli convergence weight functions Nadaraya-Watson estimator

Citation

Stute, Winfried. On Almost Sure Convergence of Conditional Empirical Distribution Functions. Ann. Probab. 14 (1986), no. 3, 891--901. doi:10.1214/aop/1176992445. https://projecteuclid.org/euclid.aop/1176992445


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