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Linear and non-linear models for censored data using scale mixtures of skew-normal distributions.

Grant number: 12/18702-9
Support type:Scholarships in Brazil - Master
Effective date (Start): March 01, 2013
Effective date (End): February 28, 2015
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Statistics
Principal researcher:Víctor Hugo Lachos Dávila
Grantee:Monique Bettio Massuia
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil


Assuming that the observations follow a normal distribution is a common assumption for linear and nonlinear models for censored responses (see Barros et al., 2010; Sharma and Agarwal, 2003). However, this assumption is not realistic, obscuring important features of the variation that is present in the data. Arabmazar and Schmidt (1982) studied the consequences of the misspecification of the distribution of errors in the Tobit model and they noticed that the asymptotic bias of maximum likelihood estimators undertaken under the assumption of normality can be significant. Thus, it is convenient to consider classes of parametric distributions that are flexible to detect a broad variety of symmetrical and asymmetrical behaviors, that include symmetric distributions as special cases and that produce robust estimations under the considered model.The class of scale mixtures of skew-normal distributions (Branco and Dey, 2001; Lachos, Ghosh and Arellano-Valle 2010) is interesting as it includes both symmetric and asymmetric version of some distributions, among which Student-t, slash, contaminated-normal and exponential power, all of which with heavier tails than the normal distribution; therefore, the estimates obtained under these models are more robust than the ones obtained under the normal model.The goal of this project is to present a study of classical and Bayesian inference in linear and nonlinear regression models for censored data under more robust distributions than the skew-normal, i.e., under the scale mixtures of skew-normal class of distributions. In addition, analysis of diagnostic of both local and global influence will be presented using the methodology of Zhu and Lee (2001). In the Bayesian context, the diagnostic analysis will be based on the divergence measure "q" (Peng and Dey, 1995), of which the Kullback-Leibler divergence is a special case (see Castro, Lachos, Arellan-Valle and Ferreira, 2012 ). In the estimation procedure we are going to use the EM algorithm and the Gibbs sampler with implementation in R and WinBUGS, respectively.This project intends to foster the development of the field of statistical research by providing new results in models of practical interest and by expanding some results found, for example, in Massuia, Cabral, Matos and Lachos (2012).

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
MASSUIA, MONIQUE B.; GARAY, ALDO M.; CABRAL, CELSO R. B.; LACHOS, V. H. Bayesian analysis of censored linear regression models with scale mixtures of skew-normal distributions. STATISTICS AND ITS INTERFACE, v. 10, n. 3, p. 425-439, 2017. Web of Science Citations: 2.

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