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A Bayesian semiparametric model for semicontinuous data

When the target variable exhibits a semicontinuous behaviour (i.e. a point mass in a single value and a continuous distribution elsewhere) parametric `two-part regression models' have been extensively used and investigated. In this paper, a semiparametric Bayesian two-part regression model for dealing with such variables is proposed. The model allows a semiparametric expression for the two part of the model by using Dirichlet processes. A motivating example (in the `small area estimation' framework) based on pseudo-real data on grapewine production in Tuscany, is used to evaluate the capabilities of the model. Results show a satisfactory performance of the suggested approach to model and predict semicontinuous data when parametric assumptions (distributional and/or relationship) are not reasonable.