The Annals of Statistics

Universally Consistent Conditional $U$-Statistics

Winfried Stute

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.

Article information

Source
Ann. Statist., Volume 22, Number 1 (1994), 460-473.

Dates
First available in Project Euclid: 11 April 2007

https://projecteuclid.org/euclid.aos/1176325378

Digital Object Identifier
doi:10.1214/aos/1176325378

Mathematical Reviews number (MathSciNet)
MR1272093

Zentralblatt MATH identifier
0818.62049

JSTOR
Stute, Winfried. Universally Consistent Conditional $U$-Statistics. Ann. Statist. 22 (1994), no. 1, 460--473. doi:10.1214/aos/1176325378. https://projecteuclid.org/euclid.aos/1176325378