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December 2011 Saddlepoint approximations for likelihood ratio like statistics with applications to permutation tests
John Kolassa, John Robinson
Ann. Statist. 39(6): 3357-3368 (December 2011). DOI: 10.1214/11-AOS945


We obtain two theorems extending the use of a saddlepoint approximation to multiparameter problems for likelihood ratio-like statistics which allow their use in permutation and rank tests and could be used in bootstrap approximations. In the first, we show that in some cases when no density exists, the integral of the formal saddlepoint density over the set corresponding to large values of the likelihood ratio-like statistic approximates the true probability with relative error of order 1/n. In the second, we give multivariate generalizations of the Lugannani–Rice and Barndorff-Nielsen or r* formulas for the approximations. These theorems are applied to obtain permutation tests based on the likelihood ratio-like statistics for the k sample and the multivariate two-sample cases. Numerical examples are given to illustrate the high degree of accuracy, and these statistics are compared to the classical statistics in both cases.


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John Kolassa. John Robinson. "Saddlepoint approximations for likelihood ratio like statistics with applications to permutation tests." Ann. Statist. 39 (6) 3357 - 3368, December 2011.


Published: December 2011
First available in Project Euclid: 5 March 2012

zbMATH: 1246.62121
MathSciNet: MR3012411
Digital Object Identifier: 10.1214/11-AOS945

Primary: 62G09 , 62G20
Secondary: 60F10

Keywords: large deviations , nonparametric tests , randomization tests

Rights: Copyright © 2011 Institute of Mathematical Statistics

Vol.39 • No. 6 • December 2011
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