Abstract
Quantile regression (QR) describes the relationship between the response variable and the exploratory variables through some specific quantiles, which has been applied to a wide range of data and different fields. Under the linear model assumption, Zou and Yuan (2008) proposed the composite quantile regression (CQR) to incorporate several quantiles at a time in the estimation function. In theory, CQR has better estimation precision when the linear model assumption holds, but it is not adequate and biased when the assumption is wrong. Without the linear model assumption, this thesis suggest a penalized quantile regression (PQR) method which implements either QR or CQR according to the empirical data property, by including a specific grouped lasso regularization term on the regression parameters in the estimation function. Simulation results show that PQR has good estimation performance over the QR and CQR under various situations.