Using Bootstrap Likelihood Ratios in Finite Mixture Models
研究了在混合模型中，当真实成分数少于模型设定时，使用似然比统计量进行统计推断的非正则问题，并证明了最大似然估计收敛于相同密度函数子集，与Aitkin和McLachlan提出的自助法相关联。
SUMMARY Statistical inference using the likelihood ratio statistic for the number of components in a mixture model is complicated when the true number of components is less than that of the proposed model since this represents a non-regular problem: the true parameter is on the boundary of the parameter space and in some cases the true parameter is in a nonidentifiable subset of the parameter space. The maximum likelihood estimator is shown to converge to the subset characterized by the same density function, and connection is made to the bootstrap method proposed by Aitkin and co-workers and McLachlan for testing the number of components in a finite mixture and deriving confidence regions in a finite mixture.