Parametric Elliptical Regression Quantiles

Abstract

The article extends linear and nonlinear quantile regression to the case of vector responses by generalizing multivariate elliptical quantiles to a regression context. In particular, it introduces parametric elliptical quantile regression in a general nonlinear multivariate heteroscedastic framework and discusses, investigates, and illustrates the new method in some detail, including basic properties, various parametrizations, possible heteroscedastic patterns, related computational issues, model validation, and a real biometric data example. The method seems suitable for multiresponse regression models with symmetric errors, especially if the dimension of responses is less than ten and if the right parametrization of the model follows from the context.