Tests for the multivariate k-sample problem based on the empirical characteristic function

Abstract

Tests for the multivariate k-sample problem are considered. The tests are based on the weighted L2 distance between empirical characteristic functions, and afford an interesting interpretation in terms of a corresponding test statistic based on the L2 distance of pairs of non-parametric density estimators. Depending on the choice of weighting, a corresponding Dirac-type weight function reduces the test to a normalised version of the L2 distance between the sample means of the k populations. Theoretical and computational issues are considered, while the finite-sample implementation based on the permutation distribution of the test statistic shows that the new test performs well in comparison with alternative procedures of the change-point type.

Keywords:

• k-sample problem
• empirical characteristic function
• non-parametric test

AMS 2000 Classification Numbers:

• 62G9
• 62G10
• 62G20

Acknowledgements

Work on this topic was partially completed while the second author was visiting Charles University of Prague (CUP). SGM wishes to sincerely thank the National and Kapodistrian University of Athens and CUP for partial financial support, and the Department of Statistics of CUP, for the hospitality. The work of the first author was supported by grants MSM113200008 and GA\v CR 201/06/0186.