An estimation method for the Neyman chi-square divergence with application to test of hypotheses

We propose a new definition of the Neyman chi-square divergence between distributions. Based on convexity properties and duality, this version of the χ2 is well suited both for the classical applications of the χ2 for the analysis of contingency tables and for the statistical tests in parametric models, for which it is advocated to be robust against outliers. We present two applications in testing. In the first one, we deal with goodness-of-fit tests for finite and infinite numbers of linear constraints; in the second one, we apply χ2-methodology to parametric testing against contamination.