Maximum likelihood methods in a robust censored errors-in-variables model

We develop a non-standard linear regression analysis by considering that the dependent variable is left censored and also that some of the explanatory variables are measured with additive errors. Our censored measurement error regression model is specified by assuming heavy-tailed distributions for the underlying probabilistic process. Specifically, we focus on assuming a multivariate joint distribution for the error terms and the unobserved true covariates. 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. We also develop an EM algorithm to obtain the estimates. The performance of the newly developed methodology is evaluated throughout a simulation study as well as a case study analysis.