On minimizing chi-square distances under the hypothesis of homogeneity or independence for a two-way contingency table

The present paper investigates estimation under the hypothesis of homogeneity or independence for a two-way contingency table. A family of optimality criteria (distances) is introduced of which well-known criteria such as maximum likelihood, Pearson- and Neyman chi-square. The Kullback-Liebler distance turn out to be special cases. We look at the convexity properties of this family and provide some general results. Give any member of this family, an analytical solution is provided for the optimal estimator under the hypothesis of homogeneity whereas a simple algorithm solution is given for the optimal row- and column margin estimators under the hypothesis of independence.