Using Implicit Function Theorem, we get the asymptotic expansion and normality of the minimum φ-divergence estimator (M φ E) which is seen to be a generalization of the maximum likelihood estimator for loglinear models under product-multinomial sampling. Then we use M φ Es 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 M φ Es and assess the finite-sample performance among different M φ Es. © 2009 Elsevier B.V. All rights reserved.
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