USING BOOTSTRAP LIKELIHOOD RATIOS IN FINITE MIXTURE-MODELS

Statistical inference using the likelihood ratio statistic for the num ber of components in a mixture model is complicated when the true numb er of components is less than that of the proposed model since this re presents 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 no nidentifiable subset of the parameter space. The maximum likelihood es timator is shown to converge to the subset characterized by the same d ensity function, and connection is made to the bootstrap method propos ed by Aitkin and co-workers and McLachlan for testing the number of co mponents in a finite mixture and deriving confidence regions in a fini te mixture.