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Applied Math Colloquium

Friday, March 28, 2014, 11:30 AM
Cullimore Lecture Hall, Lecture Hall II
New Jersey Institute of Technology

Tests of independence for sparse contingency tables and beyond

Christian Genest

McGill University, Canada

Abstract

New statistics will be proposed for testing the hypothesis that arbitrary random variables are mutually independent. These tests are consistent and well-behaved for any type of data, even for sparse contingency tables and tables whose dimension depends on the sample size. The statistics are Cramer-von Mises and Kolmogorov-Smirnov type functionals of the empirical checkerboard copula. The asymptotic behavior of the corresponding empirical process will be characterized and illustrated; it will also be shown how replicates from the limiting process can be generated using a multiplier bootstrap procedure. As will be seen through simulations, the new tests are considerably more powerful than those based on the Pearson chi-squared, likelihood ratio, and Zelterman statistics often used in this context.