Likelihood Based Inference for Censored Linear Regression Models with Scale Mixtures of Skew-Normal Distributions

In many studies the data collected are subject to some upper and lower detection limits. Hence, theresponses are either left or right censored. A complication arises when these continuous measures presentheavy tails and asymmetrical behavior, simultaneously. For such data structures, we propose a robustcensored linear model based on the scale mixtures of skew-normal (SMSN) distributions. The SMSN is anattractive 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 asspecial cases. We propose a fast estimation procedure to obtain the maximum likelihood (ML) estimatesof the parameters, using a stochastic approximation of the EM (SAEM) algorithm. This approach allowsus to estimate the parameters of interest easily and quickly, obtaining as a byproduct the standard errors,predictions of unobservable values of the response and the log-likelihood function. The proposed methodsare illustrated through a real data application and several simulation studies.