Inferences for Mixtures of Distributions for Centrally Censored Data with Partial Identification

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 (2003) 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 (2005). Our proposal of the three adapted methods is shown to provide similar inferential answers, thus offering alternative analyses.

Keywords:

• Bayesian inference
• EM algorithm
• Fiducial inference
• Gibbs sampler
• MCMC
• Middle censoring
• Profile likelihood

Mathematics Subject Classification:

• 62F10
• 62F15

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.