Conditional $U$-Statistics

Winfried Stute

doi:10.1214/aop/1176990452

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Home > Journals > Ann. Probab. > Volume 19 > Issue 2 > Article

April, 1991 Conditional $U$-Statistics

Winfried Stute

Ann. Probab. 19(2): 812-825 (April, 1991). DOI: 10.1214/aop/1176990452

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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.