Asymptotic Normality Of LAD Estimates In Two-tailed Censored Regression Models

Limited and Qualitative Dependent Variables (LDV) regression model is an important part of modern econometrics and widely applied in econometrics. The censored regression model is a special LDV model and its way of thinking is wide-ly applied in the study of many econometric problems, such as demand issues, dividend behavior, investment behavior and so on. Therefore, there are many studies on parameter estimates and inferences in Tobit regression models. Due to accuracies of measurement tools or mechanisms, response variables are limited by some maximum or minimum values, and their values larger or less than mea-surement limits can not be observed in our reality problem. However, work with response constrained by both maximum and minimum values is rare. Therefore, under this situation, we extend the traditional Tobit model to such a bilateral fixed censored regression model, which is referred to as two-tailed Tobit model.Under two-tailed Tobit model, this paper constructs the least absolute devia-tions (LAD) estimates of regression parameters and obtains statistical properties of the LAD estimates. Finally, numerical simulation studies show that the pro-posed method performs well.