Edgeworth Expansion of the Moment-Based Test for Homogeneity in an NEF-QVF Mixture Model

Abstract

In this article, we study the moment-based test procedure for a mixture distribution for the Natural exponential family with quadratic variance functions (NEF-QVF) family proposed by Ning et al. (2009b) in the small sample size scenario. We derive the approximation for the null distribution of the test statistic by the Edgeworth expansion. The simulations are conducted for a binomial mixture distribution, which includes the situation corresponding to the detection of the linkage in the genetic analysis, with different sample sizes and family sizes at various significance levels. The simulation results show that our test performs reasonably well. We also apply the proposed method to the real clinical data to verify the significant difference between two drug treatments. The critical values associated with a binomial mixture distribution are also provided.

Keywords:

• Edgeworth expansion
• Mixture distribution
• Moment-based
• NEF-QVF family
• Small sample sizes

Mathematics Subject Classification:

• Primary 62F03, 62F12
• Secondary 62H12

Acknowledgments

The authors wish to thank three referees for their helpful comments, which helped the article's clarity and crispness.