The Annals of Probability

Conditional $U$-Statistics

Winfried Stute

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Abstract

We introduce a class of so-called conditional $U$-statistics, which generalize the Nadaraya-Watson estimate of a regression function in the same way as Hoeffding's classical $U$-statistics is a generalization of the sample mean. Asymptotic normality and weak and strong consistency are proved.

Article information

Source
Ann. Probab., Volume 19, Number 2 (1991), 812-825.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990452

Digital Object Identifier
doi:10.1214/aop/1176990452

Mathematical Reviews number (MathSciNet)
MR1106287

Zentralblatt MATH identifier
0770.60035

JSTOR
links.jstor.org

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60F15: Strong theorems 62J99: None of the above, but in this section

Keywords
Conditional $U$-statistics smoothing asymptotic normality strong convergence

Citation

Stute, Winfried. Conditional $U$-Statistics. Ann. Probab. 19 (1991), no. 2, 812--825. doi:10.1214/aop/1176990452. https://projecteuclid.org/euclid.aop/1176990452


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