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June, 1985 Robust Two-Sample Permutation Tests
Diane Lambert
Ann. Statist. 13(2): 606-625 (June, 1985). DOI: 10.1214/aos/1176349542


A new two-sample randomization test is proposed for testing that the joint distribution of two samples is invariant under permutations. The $p$-value of the test has a finite sample minimaxity property over neighborhoods of completely specified alternative distributions. Asymptotically, the test has minimax Bahadur slope against the neighborhoods, which remain fixed as the sample sizes increase. The proposed test also offers the best compromise between robustness against departures from a model alternative and optimality at the model alternative in the sense that no other test with the same gross-error-sensitivity has larger slope at the model. Some modifications of the test are proposed for testing the nonparametric null hypothesis against neighborhoods of models that have a shared nuisance location-scale parameter. These nuisance-parameter-free versions of the test are justified for large samples from exponential families, and an example of their use is given.


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Diane Lambert. "Robust Two-Sample Permutation Tests." Ann. Statist. 13 (2) 606 - 625, June, 1985.


Published: June, 1985
First available in Project Euclid: 12 April 2007

zbMATH: 0582.62033
MathSciNet: MR790560
Digital Object Identifier: 10.1214/aos/1176349542

Primary: 62G35
Secondary: 62E20, 62G10

Rights: Copyright © 1985 Institute of Mathematical Statistics


Vol.13 • No. 2 • June, 1985
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