Statistics Seminar: John Robinson -- Robust permutation tests

John Robinson School of Mathematics and Statistics University of Sydney 

Location: Carslaw 173 

Time: 2pm Friday, April 30, 2010 

Title: Robust permutation tests 

Abstract: We first consider robust permutation tests for a location shift in the two
sample case based on estimating equations, comparing the test statistics based on a
score function and M-estimates.  We obtain a form for these tests so that the exact
tests may be carried out using the same algorithms as used for permutation tests based
on the mean and we obtain some numerical results indicating the increase in power when
using robust tests.  We consider asymptotics for these test statistics from which we
obtain saddlepoint approximations for tail probabilities which maintain second order
relative errors and enable us to consider Bahadur slopes of the tests based on the two
statistics.  We show that they have different Bahadur slopes with neither exceeding the
other over the whole range.  We also report some simulations confirming these large
deviation results and indicating the accuracy of the saddlepoint approximations.  We
consider extensions to the k sample robust permutation test and a two sample
multivariate test based on estimating equations.  In both cases we need to choose a test
statistic for such a multi-parameter test.  Rather than the usual sum of squares we use
a natural convex test statistic which permits an accurate saddlepoint approximation.  We
give the saddlepoint approximations and obtain some numerical results illustrating their
accuracy.