Testing equivalence of multinomial distributions -- a constrained bootstrap approach

In this paper we develop a novel bootstrap test for the comparison of two multinomial distributions. The two distributions are called {\it equivalent} or {\it similar} if a norm of the difference between the class probabilities is smaller than a given threshold. In contrast to most of the literature our approach does not require differentiability of the norm and is in particular applicable for the maximum- and $L^1$-norm.