Group variable selection and estimation in the tobit censored response model

The tobit censored response model plays an important role in analyzing the dependent variable with a constraint at a pre-specified point such as 0, and is widely used in econometrics research. For this regression model, there are few studies on variable selection in a group manner. In this paper, we present a group variable selection and estimation method for predefined groups of variables. The proposed method selects variables significantly contributing to the regression model and presents consistent estimates of parameters in the selected groups. The asymptotic properties of the resulting estimates are similar to oracle properties. The performance of our method is evaluated with extensive simulation studies and a real example from a married women’s work hour study.