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

作者：Jin Yinghua; Wu Yaohua^*

来源：Journal of Statistical Planning and Inference, 2009, 139(10): 3488-3500.

DOI：10.1016/j.jspi.2009.04.020

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

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

• 出版日期2009-10-1
• 单位中国科学技术大学