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

Abstract

We revisit the generalized hyperbolic (GH) distribution and its nested models. These include widely used parametric choices like the multivariate normal, skew‐, 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.