Estimation And Test Of Piecewise Mixed Tobit Threshold Regression Model

Threshold estimation and test is an important issue in threshold regression models.When the data is censored,the estimation of the traditional threshold regression model may be biased.The existing piecewise linear regression model can measure the linear structure,but it can not effectively capture the quadratic structure.We extend linear and quadratic structure to the censored threshold regression model and propose a piecewise mixed Tobit threshold regression model.We estimate the location of threshold,regression coefficients and the existence test of threshold in piecewise mixed Tobit threshold regression model.The main contend are as follows:(1)We propose a gird search method to optimize the objective function,and estimate the threshold location in the piecewise mixed Tobit threshold regression model with single threshold.We prove the large sample properties of parameter estimation.The large sample properties of estimation are proved.Numerical simulation results verify the validity and reliability of the estimation under different error distributions.(2)We construct the quasi-likelihood ratio statistic and prove the limit distribution of the test in the piecewise mixed Tobit threshold regression model by using the likelihood function distance of different assumptions.Numerical simulation results show the effectiveness of the test statistic under different error distributions.(3)We analyze the commercial health insurance using the above threshold location estimation and test methods.The study shows that there is a threshold for the average age of family members at 41.12.The insured amount decreases slowly and rapidly between threshold.Based on the above methods,we analyze household financial assets,river pollution and power quality and find the threshold.The analysis results show that our model and method were reliable.