Quantile estimation for multivariate data using the multivariate generalised hyperbolic distribution (R-12215)

Quantile regression is a tool to describe data distributions that is easy to understand. To estimate such quantiles, one can work with the asymmetric Laplace distribution. However, as real-life applications often involve multiple, interrelated outcomes, statistical modelling should also take this dependence into account. A possible approach is the use of the multivariate generalisation of the asymmetric Laplace distribution. This distribution itself poses some computational problems, but these could be overcome by studying the larger family of multivariate generalised hyperbolic (MGH) distributions instead, from which the multivariate asymmetric Laplace distribution can be derived as a limiting case. In this project, we study the parameters of the MGH-distribution in the context of quantile regression. This means that we investigate their influence on the (marginal) quantiles and try to estimate these parameters based on data. To realise such an estimation, one typically imposes some constraints on the parameters. Here, we focus on an approach that requires little assumptions on the parameters and is thus flexible. In a next step, we generalise this idea in order to take more information (at the same time) and complex data into account when estimating the parameters. Finally, the methodology is implemented in a computer program. This way, our new techniques can be used by other researchers as well and contribute to more accurate modelling in a multitude of contexts.

Keywords:quantile regression.

Disciplines:Statistics