Quantile regression in heteroscedastic varying coefficient models

Abstract

Varying coefficient models are flexible models to describe the dynamic structure in longitudinal data. Quantile regression, more than mean regression, gives partial information on the conditional distribution of the response given the covariates. In the literature, the focus has been so far mostly on homoscedastic quantile regression models, whereas there is an interest in looking into heteroscedastic modelling. This paper contributes to the area by modelling the heteroscedastic structure and estimating it from the data, together with estimating the quantile functions. The use of the proposed methods is illustrated on real-data applications. The finite-sample behaviour of the methods is investigated via a simulation study, which includes a comparison with an existing method.