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Biometrika 1982 69(3):619-624; doi:10.1093/biomet/69.3.619
© 1982 by Biometrika Trust
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Cramér—von Mises distributions and permutation tests

B. M. BROWN

Department of Mathematics, University of Tasmania Hobart, Tasmania, Australia

In the k-sample problem, or one-way analysis of variance, a multiple response permutation procedure based on within-group sums of absolute rank differences is shown to have a certain large sample limit distribution. This distribution is the convolution of k— 1 copies of the usual Cramér—von Mises distribution, and so is a Cramér-von Mises analogue of chi-squared. Quantiles and a simple chi-squared approximation are outlined.

Key Words: Chi-squared • Cramér-von Mises distribution • Cumulant • Legendre series • Multivariate Brownian bridge • Permutation test • Rank difference • Robustness • Weak convergence


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