Statistical Modelling 22 (6) (2022), 566–584
Quantile regression for longitudinal data via the multivariate generalized hyperbolic distribution
Alvaro J. Flórez,
DSI,
I-BioStat,
Universiteit Hasselt,
Belgium.
School of Statistics,
Universidad del Valle,
Colombia.
Ingrid Van Keilegom,
ORSTAT,
KU Leuven,
Belgium.
e-mail: ingrid.vankeilegom@kuleuven.be
Geert Molenberghs,
DSI,
I-BioStat,
Universiteit Hasselt,
Belgium.
Abstract:
While extensive research has been devoted to univariate quantile regression, this is considerably less the case for the multivariate (longitudinal) version, even though there are many potential applications, such as the joint examination of growth curves for two or more growth characteristics, such as body weight and length in infants. Quantile functions are easier to interpret for a population of curves than mean functions. While the connection between multivariate quantiles and the multivariate asymmetric Laplace distribution is known, it is less well known that its use for maximum likelihood estimation poses mathematical as well as computational challenges. Therefore, we study a broader family of multivariate generalized hyperbolic distributions, of which the multivariate asymmetric Laplace distribution is a limiting case. We offer an asymptotic treatment. Simulations and a data example supplement the modelling and theoretical considerations.
Keywords:
asymptotics, longitudinal data, maximum likelihood, pseudo-likelihood, quantile regression
Downloads:
R Code and data in zipped archive and supplementary material.
back