Variable selection and shrinkage quantile estimation for censored regression model

Censored regression (“Tobit”) model is a kind of limited dependent variable model widely used in econometrics research. Based on the quantiles estimation and the smoothly clipped absolute deviation (SCAD), a method for variable selection and shrinking estimation was presented, which selects the non-zero coefficients corresponding to the significant variables and simultaneously gives a consistent estimate of the parameters. In addition, the variable selection possesses the oracle properties. Finally, numerical studies were conducted to evaluate the performance of the proposed method for censored regression model.