Divergence-Based Estimation and Testing of Statistical Models of Classification

The problems of estimating parameters of statistical models for categorical data, and testing hypotheses about these models are studied. Asymptotic properties of estimators minimizing φ-divergence between theoretical and empirical vectors of means are established. Asymptotic distributions of φ-divergences between empirical and estimated vectors of means are explictly evaluated, and tests based on these statistics are studied. The paper extends results previously established in this area.