Study On Piecewise Linear Tobit Regression Model Inference

This paper focuses on the piecewise linear Tobit regression model.The purpose of this study is to estimate the number of change points,the value of change points and the regression coefficient in the piecewise linear Tobit regression model.Firstly,the research background,research status and research contents at home and abroad are introduced.In the second chapter,a piecewise linear Tobit regression model with a single change point is studied based on the grid search method.The test of the existence of the change point is given.Simulation results show that the estimation and test methods are effective,and the simulation results also verify the theoretical results.The grid search method has good applicability to deal with nonlinear problems,but too dense grid will aggravate the calculation accuracy and calculation time.To improve the efficiency of operation,in chapter 3,the kernel function method is proposed to study the piecewise linear Tobit regression model with a single change point.The kernel method smooths the nondifferentiable terms of the objective function by Taylor expansion,and then giving the initial values of the change point and the coefficients.The change point and other parameter estimations are obtained by iteration.The large sample properties of estimators was derived.The validity and reliability of the estimation method are verified by simulation.The empirical analysis of practical problems using the methods of this chapter shows that the change point does exist.The estimated results are more in line with the actual situation.Considering that piecewise linear Tobit regression model with a single change point is limited in application,chapter 4 studies piecewise linear Tobit regression model with multiple change points based on linearization technology.By giving the initial value of change points which is more than the actual number of change points,estimate the value of change points and other parameters by linearization technique.Then discard the abnormal change point value.And then using the BIC information criterion to select variables for change points.Finally,the estimation of the number of change points,change points and regression coefficient is obtained.The simulation results show that this method has good robustness and applicability.Finally summarized the main conclusions of this paper and the future work prospects.