Minimum φ-divergence estimator and hierarchical testing in loglinear models under product-multinomial sampling

Using Implicit Function Theorem, we get the asymptotic expansion and normality of the minimum φ-divergence estimator (MφE) which is seen to be a generalization of the maximum likelihood estimator for loglinear models under product-multinomial sampling. Then we use MφEs and φ-divergence measures to construct statistics in order to solve some classical problems including testing nested hypotheses. In last section we apply this method to a real data and do some simulation study to show the validness of MφEs and assess the finite-sample performance among different MφEs.