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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 closedform 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.

In acquired immunodeficiency syndrome (AIDS) studies it is quite common to observe viral load measurements collected irregularly over time. Moreover, these measurements can be subjected to some upper and/or lower detection limits depending on the quantification assays. A complication arises when these continuous repeated measures have a heavy-tailed behavior. For such data structures, we propose a robust structure for a censored linear model based on the multivariate Student's t-distribution. To compensate for the autocorrelation existing among irregularly observed measures, a damped exponential correlation structure is employed. An efficient expectation maximization type algorithm is developed for computing the maximum likelihood estimates, obtaining as a by-product the standard errors of the fixed effects and the log-likelihood function. The proposed algorithm uses closed-form expressions at the E-step that rely on formulas for the mean and variance of a truncated multivariate Student's t-distribution. The methodology is illustrated through an application to an Human Immunodeficiency Virus-AIDS (HIV-AIDS) study and several simulation studies.

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An extension of some standard likelihood based procedures to heteroscedastic nonlinear regression models under scale mixtures of skew-normal (SMSN) distributions is developed. We derive a simple EM-type algorithm for iteratively computing maximum likelihood (ML) estimates and the observed information matrix is derived analytically. Simulation studies demonstrate the robustness of this flexible class against outlying and influential observations, as well as nice asymptotic properties of the proposed EM-type ML estimates. Finally, the methodology is illustrated using an ultrasonic calibration data.