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.
Publié le : 1985-03-14
Classification:
$U$-Statistics,
asymptotic,
large sample,
fixed width confidence interval,
generalized mean,
sequential estimation,
efficient,
consistent,
stopping variable,
martingale,
central limit theorem,
nonparametric,
distribution free,
sample average,
62G15,
62E20
@article{1176346588,
author = {Sproule, Raymond N.},
title = {Sequential Nonparametric Fixed-Width Confidence Intervals for $U$-Statistics},
journal = {Ann. Statist.},
volume = {13},
number = {1},
year = {1985},
pages = { 228-235},
language = {en},
url = {http://dml.mathdoc.fr/item/1176346588}
}
Sproule, Raymond N. Sequential Nonparametric Fixed-Width Confidence Intervals for $U$-Statistics. Ann. Statist., Tome 13 (1985) no. 1, pp. 228-235. http://gdmltest.u-ga.fr/item/1176346588/