The Annals of Statistics

Asymptotic Expansions for the Power of Distributionfree Tests in the Two-Sample Problem

P. J. Bickel and W. R. van Zwet

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Abstract

Asymptotic expansions are established for the power of distribution-free tests in the two-sample problem. These expansions are then used to obtain deficiencies in the sense of Hodges and Lehmann for distribution-free tests with respect to their parametric competitors and for the estimators of shift associated with these tests.

Article information

Source
Ann. Statist., Volume 6, Number 5 (1978), 937-1004.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344305

Digital Object Identifier
doi:10.1214/aos/1176344305

Mathematical Reviews number (MathSciNet)
MR499567

Zentralblatt MATH identifier
0378.62047

JSTOR
links.jstor.org

Subjects
Primary: 62G10: Hypothesis testing
Secondary: 62G20: Asymptotic properties 60F05: Central limit and other weak theorems

Keywords
Distributionfree tests linear rank tests permutation test Hodges-Lehmann estimators power contiguous alternatives asymptotic expansions Edgeworth expansions deficiency rejective sampling sampling without replacement

Citation

Bickel, P. J.; van Zwet, W. R. Asymptotic Expansions for the Power of Distributionfree Tests in the Two-Sample Problem. Ann. Statist. 6 (1978), no. 5, 937--1004. doi:10.1214/aos/1176344305. https://projecteuclid.org/euclid.aos/1176344305


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