Modelos de regressão t-Tobit com erros nas covariáveis

Abstract

In this work, we develop a non-standard linear regression analysis by considering that the dependent variable is censored and also that some of the explanatory variables are measured with additive errors. In addition, our censored measurement error regression model is speci ed by assuming heavy-tailed distributions for the underlying probabilistic process. Speci cally, our analysis focuses on assuming a multivariate Student-t joint distribution for the error terms and the unobserved true covariates. In this sense, the proposed model will be robust enough to protect our inferences of atypical or in uential observations. For the model estimation, we consider the maximum likelihood methodology, in which we include the estimation of the asymptotic variance of the maximum likelihood estimators and we also develop an EM type algorithm to obtain the estimates, and also the Bayesian paradigm, in which we use a data augmentation approach and develop a MCMC algorithm to sample from the posterior distributions. The proposed methodology is exible enough to be adapted for heavy-tailed distributions coming from the class of scale mixture of the normal distribution. The performance of the newly developed methodology is evaluated throughout a Monte Carlo study as well as a case sudy analysis.