Statistical Inference And Application In Continuous Threshold Linear Quantile Regression Model

This thesis is devoted to explore continuous threshold linear regression model.We study the problems of testing for change points and estimating and inferencing for parameters in model.Change-point problem is widely used in economic,financial,epidemiology,biomedical,artificial intelligence and environment and other areas since the 1950's.It is very important to study change-point problem by contemporary statistical method since regression model with change points has been widely developed and applied in practical in recent years.The research for change point problem focuses on two aspects.One is to detect the existence of change point and then to determine the number of change points.The other is to estimate the change-point and other parameters in model.In the regression model setting,the change points can be divided into continuous or discontinuous points according to the regression function is continuous or discontinuous at change points.This thesis aims to study continuous threshold quantile regression model,which allowing for one or multiple change points in a covariate.The performances and results of our study are mainly described as following.In Chapter 2,based on a simple linearization,we proposed an new estimation procedure technique for bent line quantile regression model.The proposed method can estimate the regression coefficients and change point simultaneously.In addition,we can easily construct the confidence interval of proposed estimator from the theory of standard linear quantile regression model and the delta technique.A lot of simulation results demonstrate that the proposed estimation method is validity.At the last,we apply the model and proposed method to two real data analysis.We continue to study bent line quantile regression model in Chapter 3.In Chapter2,we adopt a linearization technique to propose a new method for estimating parameters in model.That proposed method could simultaneously estimate the regression coefficients and change point,however,it has the disadvantage of underestimating change point.So we develop a new procedure for estimating all parameters via a smooth technique.We establish the asymptotic properties of the proposed estimator.Furthermore,a formal test procedure for testing the existence of the change point is presented.The results from numerical simulation and the analysis of a real data demonstrate that the proposed method has effective and feasible performances.In Chapter 4,we gradually extend bent line quantile regression model onto the topic of continuous threshold quantile regression model with multiple change points.We first proposed an new method to estimate change points parameters and regression coefficients via a bent-cable smoothing technique for fixed number of change points.In the meantime,the asymptotic properties of the proposed estimator are established.In a next step,we introduce an easy modified wild binary segmentation algorithm with low computational complexity to determine the number of change points for continuous threshold quantile regression model.The performances of proposed estimator and test procedure are investigated by numerical simulation.The analysis of two real data set is provided for illustrative purpose.In Chapter 5,we extend the estimation method in Chapter 2 onto the bent line expectile regression model.In this chapter,we adopt a simple linearization technique for estimating parameters and obtain the confidence intervals based on the theory of standard linear expectile regression model and delta technique.The proposed estimation procedure is easy implemented by current software.The numerical simulation and the real data analysis are both illustrated the performances of proposed estimation method.In the last Chapter,we summarize this thesis and present the further study.