Modified likelihood ratio test for homogeneity in bivariate normal mixtures with presence of a structural parameter

This paper investigates the asymptotic properties of the modified likelihood ratio statistic for testing homogeneity in bivariate normal mixture models with an unknown structural parameter. It is shown that the modified likelihood ratio statistic has χ ₂² null limiting distribution. This work was supported by the National Natural Science Foundation of China (Grant No. 10661003), the Natural Science Foundation of Guangxi (Grant No. 0728092) and SRF for ROCS, SEM (Grant No. [2004]527)