Open Access
July, 1986 On Almost Sure Convergence of Conditional Empirical Distribution Functions
Winfried Stute
Ann. Probab. 14(3): 891-901 (July, 1986). DOI: 10.1214/aop/1176992445


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 $Y$.


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Winfried Stute. "On Almost Sure Convergence of Conditional Empirical Distribution Functions." Ann. Probab. 14 (3) 891 - 901, July, 1986.


Published: July, 1986
First available in Project Euclid: 19 April 2007

zbMATH: 0593.60043
MathSciNet: MR841591
Digital Object Identifier: 10.1214/aop/1176992445

Primary: 60F15
Secondary: 62G05 , 62J02

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

Rights: Copyright © 1986 Institute of Mathematical Statistics

Vol.14 • No. 3 • July, 1986
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