Estimation And Test Of Piecewise Linear Censored Quantile Regression Model

This paper consider the piecewise linear censored quantile regression model with unknown change points.We estimate the number of change pionts,the loation of change points and other parameters for censored quantile regression model.A test procedure for testing the existence of change pionts are proposed.The main contend are as follows:In Chapter 2,we propose a smooth kernel function to simultaneously estimate the change point and model parameter for piecewise linear censored quantile regression model via iter ation,the limiting distribution of the proposed estimator is derived.Numerical simulation verifies the validity and reliability of our method,and the proposed method is applied to analyze a set of dala for drug treatment study data,it was found that the time interval of drug recurrence was positively correlated with the treatment time,and there were change points in the influencing factors.In Chapter 3,we study the censored quantile regression model with multiple change points with using linearization technique.When the number of change points are known,Bootstrap sample iterative updating algorithm is used to solve the selection dependence problem of initial values,the location of change points and model parameter are estimated simultaneously.When the number of change points are unknown,the number of change points are determined via reverse elimination of BIC criterion by given initial value of change points which is much larger than true value of change points.The asymptotic properties of paramters and change points are arrived.The method improve the accuracy and consistency of the number of change points and the location estimation.Simulation studies show that the proposed method is effective and robustness.This method is applied to make an empirical analysis of household financial assets data and give a reasonable explanation of the change point.In Chapter 4,a statistics of change point test is constructed based on residual-weighted CUSUM under the framework of the censored quantile regression model,and the properties of large samples are derived.Numerical simulation results show that the significance level of rejecting alternative hypothesis is about 5% when there is no change point.Finally,the main conclusions of this paper are summarized and the future research direction is given.