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March, 1994 Universally Consistent Conditional $U$-Statistics
Winfried Stute
Ann. Statist. 22(1): 460-473 (March, 1994). DOI: 10.1214/aos/1176325378

Abstract

We introduce a general class of conditional $U$-statistics and present sufficient conditions for their universal consistency in $r$th mean. It is shown that under mild assumptions on the smoothing parameters, window and $k_n$-nearest neighbor estimators are universally consistent. An application to a new nonparametric discrimination problem is also included.

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Winfried Stute. "Universally Consistent Conditional $U$-Statistics." Ann. Statist. 22 (1) 460 - 473, March, 1994. https://doi.org/10.1214/aos/1176325378

Information

Published: March, 1994
First available in Project Euclid: 11 April 2007

zbMATH: 0818.62049
MathSciNet: MR1272093
Digital Object Identifier: 10.1214/aos/1176325378

Subjects:
Primary: 62G05
Secondary: 62G07

Rights: Copyright © 1994 Institute of Mathematical Statistics

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Vol.22 • No. 1 • March, 1994
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