The Annals of Statistics

Efficient and adaptive nonparametric test for the two-sample problem

Gilles R. Ducharme and Teresa Ledwina

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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.

Article information

Ann. Statist., Volume 31, Number 6 (2003), 2036-2058.

First available in Project Euclid: 16 January 2004

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Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing 62G20: Asymptotic properties
Secondary: 62G99: None of the above, but in this section

Adaptive test efficient test model selection nonparametric test two-sample problem


Ducharme, Gilles R.; Ledwina, Teresa. Efficient and adaptive nonparametric test for the two-sample problem. Ann. Statist. 31 (2003), no. 6, 2036--2058. doi:10.1214/aos/1074290336.

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