About divergence-based goodness-of-fit tests in the dirichlet-multinomial model
- 1 January 1996
- journal article
- research article
- Published by Taylor & Francis in Communications in Statistics - Theory and Methods
- Vol. 25 (5) , 1119-1133
- https://doi.org/10.1080/03610929608831752
Abstract
The Pearson X2 statistic, the loglikelihood ratio statistic, the Freeman-Tukey statistic, and others well known statistics are considered as particular cases of appropriately normed (φ-divergences Dφ(FNF) between empirical and hypothetical distributions. All these statistics are asymptotically x2-distributed. For the Dirichlet-multinomial F, conditions on J are found under which the first two moments of the test statistics match the moments of x2, up to terms of order N--1. By calculating the exact sizes and powers of goodness-of-fit tests for 14 selected φ-divergence statistics it is shown that these conditions are of practical importance even for small sample sizes N.Keywords
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