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

  • Jin Y
  • Wu Y
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Abstract

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.

Author-supplied keywords

  • Asymptotic expansion
  • Asymptotic normality
  • Loglinear model
  • Minimum φ-divergence estimator
  • Nested hypotheses
  • φ-Divergence measure

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Authors

  • Yinghua Jin

  • Yaohua Wu

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