Linear censored regression models with scale mixtures of normal distributions

Author(s)

Garay, Aldo M. ; Lachos, Victor H. ; Bolfarine, Heleno ; Cabral, Celso R. B.

• Document type: Journal article
• Source: STATISTICAL PAPERS; v. 58, n. 1, p. 247-278, MAR 2017.
• Web of Science Citations: 11

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. (AU)

• FAPESP's process: 14/02938-9 - Estimation and diagnostics for censored mixed effects models using scale mixtures of skew-normal distributions
• Grantee: Víctor Hugo Lachos Dávila
• Support Opportunities: Regular Research Grants
• FAPESP's process: 13/21468-0 - Measurement error-in-variables models for censored data using scale mixtures of skew-normal distributions
• Grantee: Aldo William Medina Garay
• Support Opportunities: Scholarships in Brazil - Post-Doctoral