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December 2003 Efficient and adaptive nonparametric test for the two-sample problem
Gilles R. Ducharme, Teresa Ledwina
Ann. Statist. 31(6): 2036-2058 (December 2003). DOI: 10.1214/aos/1074290336


The notion of efficient test for a Euclidean parameter in a semiparametric model was introduced by Stein [Proc. Third Berkeley Symp. Math. Statist. Probab. 1 (1956) 187-195]. Such tests are locally most powerful for a wide class of infinite-dimensional nuisance parameters. The first formal application of this notion to a suitably parametrized two-sample problem was provided by Hájek [Ann. Math. Statist. 33 (1962) 1124-1147]. However, this and subsequent solutions appear to be not well-suited for practical applications. This article aims to show that an adaptive two-sample test introduced recently by Janic-Wróblewska and Ledwina [Scand. J. Statist. 27 (2000) 281-297] is locally most powerful under a more realistic setting.


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Gilles R. Ducharme. Teresa Ledwina. "Efficient and adaptive nonparametric test for the two-sample problem." Ann. Statist. 31 (6) 2036 - 2058, December 2003.


Published: December 2003
First available in Project Euclid: 16 January 2004

zbMATH: 1065.62079
MathSciNet: MR2036399
Digital Object Identifier: 10.1214/aos/1074290336

Primary: 62G10 , 62G20
Secondary: 62G99

Keywords: Adaptive test , efficient test , Model selection , Nonparametric test , two-sample problem

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 6 • December 2003
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