Heteroscedastic replicated measurement error models under asymmetric heavy-tailed distributions

We propose a heteroscedastic replicated measurement error model based on the class of scale mixtures of skew-normal distributions, which allows the variances of measurement errors to vary across subjects. We develop EM algorithms to calculate maximum likelihood estimates for the model with or without equation error. An empirical Bayes approach is applied to estimate the true covariate and predict the response. Simulation studies show that the proposed models can provide reliable results and the inference is not unduly affected by outliers and distribution misspecification. The method has also been used to analyze a real data of plant root decomposition.