  We revisit the generalized hyperbolic (GH) distribution and its nested
models. These include widely used parametric choices like the multivariate
normal, skew-t, Laplace, and several others. We also introduce the
multiple-choice LASSO, a novel penalized method for choosing among alternative
constraints on the same parameter. A hierarchical multiple-choice LASSO
penalized likelihood is optimized to perform simultaneous model selection and
inference within the GH family. We illustrate our approach through a simulation
study. The methodology proposed in this paper has been implemented in R
functions which are available as supplementary material.
