In this paper, we shall represent a generalized Chernoff-Savage statistic as the sum of i.i.d. random variables plus a remainder term and analyze the order of magnitude of the remainder term. While Chernoff and Savage have proved that the remainder term, when suitably normalized, converges to O in probability, we obtain a stronger form of convergence in this paper. Our result gives an invariance principle and a law of the iterated logarithm for generalized Chernoff-Savage statistics. We also use our result to obtain asymptotic approximations for the stopping rules of certain sequential rank tests.
Publié le : 1975-07-14
Classification:
Chernoff-Savage theorem,
sequential rank tests,
Lehmann alternatives,
Wilcoxon tests,
empirical distribution function,
large deviation probabilities,
invariance principle,
last time,
62E20,
62L10,
62G10
@article{1176343185,
author = {Lai, Tze Leung},
title = {On Chernoff-Savage Statistics and Sequential Rank Tests},
journal = {Ann. Statist.},
volume = {3},
number = {1},
year = {1975},
pages = { 825-845},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343185}
}
Lai, Tze Leung. On Chernoff-Savage Statistics and Sequential Rank Tests. Ann. Statist., Tome 3 (1975) no. 1, pp. 825-845. http://gdmltest.u-ga.fr/item/1176343185/