Likelihood-based inference for censored linear regression models with scale mixtures of skew-normal distributions

ABSTRACT

In many studies, the data collected are subject to some upper and lower detection limits. Hence, the responses are either left or right censored. A complication arises when these continuous measures present heavy tails and asymmetrical behavior; simultaneously. For such data structures, we propose a robust-censored linear model based on the scale mixtures of skew-normal (SMSN) distributions. The SMSN is an attractive class of asymmetrical heavy-tailed densities that includes the skew-normal, skew-t, skew-slash, skew-contaminated normal and the entire family of scale mixtures of normal (SMN) distributions as special cases. We propose a fast estimation procedure to obtain the maximum likelihood (ML) estimates of the parameters, using a stochastic approximation of the EM (SAEM) algorithm. This approach allows us to estimate the parameters of interest easily and quickly, obtaining as a byproducts the standard errors, predictions of unobservable values of the response and the log-likelihood function. The proposed methods are illustrated through real data applications and several simulation studies.

KEYWORDS:

• Censored regression models
• heavy tails
• SAEM algorithm
• scale mixtures of skew-normal distributions

Acknowledgments

The authors are grateful to the editor, associate editor and two referees for their helpful comments on an earlier version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research of Aldo M. Garay was supported by Grant no. 2013/21468-0 from Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) – Brazil and by Grant no. 420082/2016-6 from Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) – Brazil. Thalita B. Mattos was supported by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES).