Minimum ϕϕ-divergence estimation in misspecified multinomial models

The consequences of model misspecification for multinomial data when using minimum ϕϕ-divergence or minimum disparity estimators to estimate the model parameters are considered. These estimators are shown to converge to a well-defined limit. Two applications of the results obtained are considered. First, it is proved that the bootstrap consistently estimates the null distribution of certain class of test statistics for model misspecification detection. Second, an application to the model selection test problem is studied. Both applications are illustrated with numerical examples.

► Minimum ϕϕ-divergence estimators in multinomial populations.
► Consistency and asymptotic normality under model misspecification.
► Approximation of the null distribution of goodness-of-fit tests for multinomial data.
► Model selection test problem for grouped data.