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.
Citation
Winfried Stute. "Conditional $U$-Statistics." Ann. Probab. 19 (2) 812 - 825, April, 1991. https://doi.org/10.1214/aop/1176990452
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