## The Annals of Statistics

### Sequential Nonparametric Fixed-Width Confidence Intervals for $U$-Statistics

Raymond N. Sproule

#### Abstract

A sequential fixed-width confidence interval for the mean of a $U$-statistic, having coverage probability approximately equal to preassigned $\alpha$, is presented. The main result, Theorem 2, shows that the sequential procedure is asymptotically efficient in the sense of Chow and Robbins (1965) and assumes only finiteness of the second moment of the kernel, the weakest possible condition. The paper follows naturally from Sproule (1974) and Sproule (1969), the primary reference.

#### Article information

Source
Ann. Statist., Volume 13, Number 1 (1985), 228-235.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176346588

Digital Object Identifier
doi:10.1214/aos/1176346588

Mathematical Reviews number (MathSciNet)
MR773163

Zentralblatt MATH identifier
0595.62042

JSTOR
Sproule, Raymond N. Sequential Nonparametric Fixed-Width Confidence Intervals for $U$-Statistics. Ann. Statist. 13 (1985), no. 1, 228--235. doi:10.1214/aos/1176346588. https://projecteuclid.org/euclid.aos/1176346588