Open Access
July, 1975 On Chernoff-Savage Statistics and Sequential Rank Tests
Tze Leung Lai
Ann. Statist. 3(4): 825-845 (July, 1975). DOI: 10.1214/aos/1176343185


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.


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Tze Leung Lai. "On Chernoff-Savage Statistics and Sequential Rank Tests." Ann. Statist. 3 (4) 825 - 845, July, 1975.


Published: July, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0331.62059
MathSciNet: MR388615
Digital Object Identifier: 10.1214/aos/1176343185

Primary: 62E20
Secondary: 62G10 , 62L10

Keywords: Chernoff-Savage theorem , Empirical distribution function , invariance principle , large deviation probabilities , last time , Lehmann alternatives , sequential rank tests , Wilcoxon tests

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 4 • July, 1975
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