ABSTRACT
In this chapter we study the importance of the estimators based on φ-divergences as well as the test statistics based on φ-divergences in some classical problems of contingency tables. First, we study the problems of independence, symmetry, marginal homogeneity
and quasi-symmetry in a two-way contingency table and then the classical problem of
homogeneity. There are different approaches to these problems but we study them using the result given in Section 5.5 in Chapter 5 regarding the minimum φ-divergence estimator with constraints as well as the result given in Section 6.3.5 in Chapter 6 regarding
the testing problem when the null hypothesis can be written in terms of some constraints
on the parameter space.
