Censored and quantile regression estimation in two-part models for censored semi-continuous data

Data with an abundance of zeros arise on many occasions. Traditional statistical methods often cannot deal with this data which can be called zero-inflated data. The zero inflation caused by censored zero is often modeled by the Tobit model. However, when the distribution of the error term is not normal, the maximum likelihood estimator of the Tobit model is inconsistent. In this study, a generalization of the Tobit model based on the extended normal distribution with two additional shape parameters is proposed. In addition, the two-part model is used for modelling the zero inflation caused by real zero. The inflations caused by real zero on the left and the censoring point on the right are investigated for semi-continuous data in this study. The proposed generalized censored regression model is adjusted to the two-part model, moreover, the two-part quantile regression modelling framework is also modified for censored semi-continuous data. Two new models, the two-part generalized censored regression model and the two-part quantile regression model are introduced for censored semi-continuous data. For estimating the parameters of models, maximum likelihood estimators are obtained. The estimation process is conducted using the Expectation-Maximization (EM) algorithm. The performance of maximum likelihood estimators is evaluated by the Monte Carlo experiments. The proposed estimators are also applied to the Istanbul Chamber of Industry export data for an econometrical data example and wild boar dispersal data for an environmental data example.