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January, 1974 Asymptotic Sufficiency of the Vector of Ranks in the Bahadur Sense
Jaroslav Hajek
Ann. Statist. 2(1): 75-83 (January, 1974). DOI: 10.1214/aos/1176342614


We shall consider the hypothesis of randomness under which two samples $X_1, \cdots, X_n$ and $Y_1, \cdots, Y_m$ have an identical but arbitrary continuous distribution. The vector of ranks $(R_1, \cdots, R_{n+m})$ will be shown to be asymptotically sufficient in the Bahadur sense for testing randomness against a general class of two-sample alternatives, simple ones as well as composite ones. In other words, the best exact slope will be attainable by rank statistics, uniformly throughout the alternative.


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Jaroslav Hajek. "Asymptotic Sufficiency of the Vector of Ranks in the Bahadur Sense." Ann. Statist. 2 (1) 75 - 83, January, 1974.


Published: January, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0286.62026
MathSciNet: MR356355
Digital Object Identifier: 10.1214/aos/1176342614

Keywords: Asymptotic sufficiency of ranks , Bahadur's exact slopes , large deviations , laws of large numbers

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 1 • January, 1974
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