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 modifi...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 χ22 null limiting distribution.展开更多
Finite mixture models are widely used in scientific investigations.Due to their non-regularity,there are many technical challenges concerning inference problems on various aspects of the finitemixture models.After dec...Finite mixture models are widely used in scientific investigations.Due to their non-regularity,there are many technical challenges concerning inference problems on various aspects of the finitemixture models.After decades of effort by statisticians,substantial progresses are recorded recently in characterising large sample properties of some classical inference methods when applied to finitemixture models,providing effective numerical solutions formixture model-based data analysis,and the invention of novel inference approaches.This paper aims to provide a comprehensive summary on large sample properties of some classical statistical methods and recently developed modified likelihood ratio test and EM-test for the order of the finite mixture model.The presentation de-emphasises the rigour in order to gain some insights behind some complex technical issues.The paper wishes to recommend the EM-test as the most promising approach to data analysis problems from all models with mixture structures.展开更多
基金the National Natural Science Foundation of China (Grant No. 10661003)the Natural Science Foundation of Guangxi (Grant No. 0728092) SRF for ROCS, SEM (Grant No. [2004]527)
文摘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 χ22 null limiting distribution.
基金The author likes to thank research fundings from the National Natural Science Foundation of China(Grant No 11690011)theNatural Science and Engineering Research Council(RGPIN-2014-03743).
文摘Finite mixture models are widely used in scientific investigations.Due to their non-regularity,there are many technical challenges concerning inference problems on various aspects of the finitemixture models.After decades of effort by statisticians,substantial progresses are recorded recently in characterising large sample properties of some classical inference methods when applied to finitemixture models,providing effective numerical solutions formixture model-based data analysis,and the invention of novel inference approaches.This paper aims to provide a comprehensive summary on large sample properties of some classical statistical methods and recently developed modified likelihood ratio test and EM-test for the order of the finite mixture model.The presentation de-emphasises the rigour in order to gain some insights behind some complex technical issues.The paper wishes to recommend the EM-test as the most promising approach to data analysis problems from all models with mixture structures.
