ON THE LIKELIHOOD RATIO TEST FOR A SINGLE MODEL AGAINST THE MIXTURE OF TWO KNOWN DENSITIES

Abstract

In this paper, we consider the likelihood ratio test for a single model against the mixture of two known densities. We research the accuracy of the limiting null distribution obtained by Titterington 1-2.After that, we improve the limiting null distribution and confirm its usefulness by the simulation study.

Keywords:

• Mixture model
• Likelihood ratio test
• Limiting null distribution
• Chi-bar-squared distribution

ACKNOWLEDGMENTS

The author would like to thank Professor Chihiro Hirotsu, Professor Fumiyasu Komaki, Dr. Motoaki Kawanabe and Dr. Hisayuki Hara for helpful comments on this paper. The author also would like to give sincere thanks to anonymous referees for their useful suggestions on this paper.