Kwantielschatting voor multivariate data via de multivariate veralgemeende hyperbolische verdeling

Quantile regression provides a rich tool for describing data distributions and allows an easy interpretation. The estimation of quantiles can be translated to the maximum likelihood framework for an asymmetric Laplace distribution. But since real-life applications often involve multiple, interrelated outcomes, statistical modelling should take this dependence into account. A possible approach is the use of the multivariate generalisation of the asymmetric Laplace distribution suggested in earlier literature. Though theoretically appealing, numerically this distribution poses some problems. However, the larger parametric family of multivariate generalised hyperbolic (MGH) distributions, with special limiting case the multivariate asymmetric Laplace distribution, can provide a solution. In this project, we take a novel look at the MGH distribution in the context of quantile regression. This involves investigating the influence of the parameters on the (marginal) quantiles as well as estimating these parameters. The focus for this estimation is on flexible nonparametric approaches that do not impose strong parametric assumptions on the functional form of the parameters. Thus, we develop new semiparametric methodology for quantile estimation in complex multivariate data. The proposed estimators are studied asymptotically and generalised to multiple covariates in an additive way. Our implementation of the new techniques can improve modelling in a multitude of contexts.