The generalized hyperbolic family and automatic model selection through the multiple-choice LASSO

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 Least Absolute Shrinkage and Selection Operator (LASSO) penalized likelihood is optimized to perform simultaneous model selection and inference within the GH family. We illustrate our approach through a simulation study and a real data example. The methodology proposed in this paper has been implemented in R functions which are available as supplementary material.