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