Quantile Regression Coefficients Modeling: a Penalized Approach

Modeling quantile regression coefficients functions permits describing the coefficients of a quantile regression model as parametric functions of the order of the quantile. This approach has numerous advantages over standard quantile regression, in which different quantiles are estimated one at the time: it facilitates estimation and inference, improves the interpretation of the results, and is statistically efficient. On the other hand, it poses new challenges in terms of model selection. We describe a penalized approach that can be used to identify a parsimonious model that can fit the data well. We describe the method, and analyze the dataset that motivated the present paper. The proposed approach is implemented in the qrcmNP package in R.