About divergence-based goodness-of-fit tests in the dirichlet-multinomial model

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(F_NF) 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:

• Goodness-of-fit
• Divergence-based testing
• Moment-matching property
• Dirichlet-multinomial distribution

Additional information

Notes on contributors

M.L. Menéndez

D. Morales

L. Pardo