Ricerc@Sapienza

This research project proposes a maximum-likelihood approach to jointly estimate marginal conditional quantiles
of multivariate response variables in a linear regression framework. We consider a slight reparameterization
of the Multivariate Asymmetric Laplace distribution proposed by Kotz et al (2001) and exploit
its location-scale mixture representation to implement a new EM algorithm for estimating model
parameters. The idea is to extend the link between the Asymmetric Laplace distribution and the
well-known univariate quantile regression model to a multivariate context, i.e. when a multivariate
dependent variable is concerned. The approach accounts for association among multiple responses
and study how the relationship between responses and explanatory variables can vary across different
quantiles of the marginal conditional distribution of the responses. A penalized version of the EM
algorithm is also presented to tackle the problem of variable selection. The validity of our approach will be
analyzed in a simulation study, where we will provide evidence on the efficiency gain of the proposed
method compared to estimation obtained by separate univariate quantile regressions. Several applied fields will be considered in the project, in particular financial, environmental and economics.