Linear censored regression models with scale mixtures of normal distributions

Aldo M. Garay (), Victor H. Lachos, Heleno Bolfarine and Celso R. B. Cabral
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Aldo M. Garay: Rua Sérgio Buarque de Holanda, 651 – Cidade Universitária Zeferino Vaz Campinas
Victor H. Lachos: Rua Sérgio Buarque de Holanda, 651 – Cidade Universitária Zeferino Vaz Campinas
Heleno Bolfarine: Universidade de São Paulo
Celso R. B. Cabral: Universidade Federal do Amazonas

Statistical Papers, 2017, vol. 58, issue 1, No 13, 247-278

Abstract: Abstract In the framework of censored regression models the random errors are routinely assumed to have a normal distribution, mainly for mathematical convenience. However, this method has been criticized in the literature because of its sensitivity to deviations from the normality assumption. Here, we first establish a new link between the censored regression model and a recently studied class of symmetric distributions, which extend the normal one by the inclusion of kurtosis, called scale mixtures of normal (SMN) distributions. The Student-t, Pearson type VII, slash, contaminated normal, among others distributions, are contained in this class. A member of this class can be a good alternative to model this kind of data, because they have been shown its flexibility in several applications. In this work, we develop an analytically simple and efficient EM-type algorithm for iteratively computing maximum likelihood estimates of the parameters, with standard errors as a by-product. The algorithm has closed-form expressions at the E-step, that rely on formulas for the mean and variance of certain truncated SMN distributions. The proposed algorithm is implemented in the R package SMNCensReg. Applications with simulated and a real data set are reported, illustrating the usefulness of the new methodology.

Keywords: Censored regression model; EM-type; Algorithms; Scale mixtures of normal distributions; Outliers (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s00362-015-0696-9

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