Change-point models in quantile regression

Change-point models, in which the mean of a statistical distribution is subject to change at an unknown time point, have been studied by a great number of authors over the past half-century. Such models have applications in a wide range of areas such as allometry, dose response trials, and quality control for industrial processes. In this thesis, we study a change-point quantile regression model where the conditional quantile function is piecewise linear with a single change-point but still continuous in an independent variable. Estimation and inferential procedures are developed for this model with cross-sectional data and longitudinal data. Three tests for the presence of a change-point are proposed in the situation of independent data as well. Simulations present the finite sample performances of the inferential procedures and the tests. Applications to an example of terrestrial mammals' maximal running speeds and an Alzheimer's disease data example demonstrate practical utilities of the change-point quantile regression model.