Conditionally Parametric Quantile Regression

Abstract

Chapter 2 demonstrated that nonparametric approaches can easily be adapted to quantile regression models. In the case of a single explanatory variable, x, all that is necessary to make the model nonparametric is to add a kernel weight function $$ k\left({\left({x - x_{t} } \right)/h} \right) $$ when estimating a quantile regression for a target point $$ x_{t} $$. After estimating the function for a series of target points, the estimates can then be interpolated to all values of x. The nonparametric approach is a flexible way to add nonlinearity to the estimated quantile regressions.