Abstract
In this article, several methods to make inferences about the parameters of a finite mixture of distributions in the context of centrally censored data with partial identification are revised. These methods are an adaptation of the work in Contreras-Cristán, Gutiérrez-Peña, and O'Reilly (Citation2003) in the case of right censoring. The first method focuses on an asymptotic approximation to a suitably simplified likelihood using some latent quantities; the second method is based on the expectation-maximization (EM) algorithm. Both methods make explicit use of latent variables and provide computationally efficient procedures compared to non-Bayesian methods that deal directly with the full likelihood of the mixture appealing to its asymptotic approximation. The third method, from a Bayesian perspective, uses data augmentation to work with an uncensored sample. This last method is related to a recently proposed Bayesian method in Baker, Mengersen, and Davis (Citation2005). Our proposal of the three adapted methods is shown to provide similar inferential answers, thus offering alternative analyses.
Acknowledgments
The authors thank an anonymous referee for his helpful comments and suggestions, which led to improvements of our work. The research of Alberto Contreras-Cristán has been funded by PAPIIT grant IN109906 and by CONACyT grant J48538. Federico O'Reilly and Alberto Contreras-Cristán gratefully acknowledge support from Sistema Nacional de Investigadores Mexico.