Noel Cressie and Leandro Pardo (2000). Minimum ø-divergence estimator and hierarchical testing in loglinear models. Vol.10, No.3.

Statistica Sinica 10(2000), 867-884

MINIMUM $\phi$ -DIVERGENCE ESTIMATOR AND

HIERARCHICAL TESTING IN LOGLINEAR MODELS

Noel Cressie and Leandro Pardo

The Ohio State University and Complutense University of Madrid

Abstract: In this paper we consider inference based on very general divergence measures, under assumptions of multinomial sampling and loglinear models. We define the minimum $\phi$ -divergence estimator, which is seen to be a generalization of the maximum likelihood estimator. This estimator is then used in a $\phi$ -divergence goodness-of-fit statistic, which is the basis of two new statistics for solving the problem of testing a nested sequence of loglinear models.

Key words and phrases: Asymptotic distributions, Framinghan heart study, multinomial distribution, nested hypotheses, power divergence, Renyi divergence.