A heteroscedastic measurement error model based on skew and heavy-tailed distributions with known error variances

In this paper, we study inference in a heteroscedastic measurement error model with known error variances. Instead of the normal distribution for the random components, we develop a model that assumes a skew-t distribution for the true covariate and a centred Student's t distribution for the error terms. The proposed model enables to accommodate skewness and heavy-tailedness in the data, while the degrees of freedom of the distributions can be different. Maximum likelihood estimates are computed via an EM-type algorithm. The behaviour of the estimators is also assessed in a simulation study. Finally, the approach is illustrated with a real data set from a methods comparison study in Analytical Chemistry.