Multivariate regression quantiles in econometrics

We want to conduct some meaningful and fruitful econometric research into multivariate regression quantiles. In particular, we intend (a) to define and investigate new multivariate (regression) quantiles, especially elliptical (regression) quantiles and (regression) quantiles defined by means of polar or spherical coordinate systems (b) to explore asymptotic properties and usefulness of some statistics based on multivariate (regression) quantiles (c) to overcome related computational issues and to implement new methods in a suitable software environment (d) to illustrate some use of new multivariate regression quantiles in econometrics, e.g. in risk measurement.