Exact Nonparametric Two-Sample Homogeneity Tests
Jean‐Marie Dufour, Abdeljelil Farhat · Birkhäuser Boston eBooks · 2002
In this paper, we study several tests for the equality of two unknown distributions. Two are based on empirical distribution functions, three on nonparametric probability density estimates, and the last ones on differences between sample moments. We suggest controlling the size of such tests (under nonparametric assumptions) by using permutational versions of the tests jointly with the method of Monte Carlo tests properly adjusted to deal with discrete distributions. In a simulation experiment, we show that this technique provides perfect control of test size, in contrast with usual asymptotic critical values.