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 and a real data example about pre-term infants. The methodology proposed in this paper has been implemented in R functions which are available as supplementary material.

翻译：我们重新审视了广义双曲（GH）分布及其嵌套模型，这些模型包括多元正态分布、偏斜t分布、拉普拉斯分布等多种广泛使用的参数化选择。同时，我们引入了多元选择LASSO——一种针对同一参数上不同约束条件进行选择的新型惩罚方法。通过优化层次化多元选择LASSO惩罚似然，我们在GH族内实现了同步的模型选择与推断。我们通过模拟研究和关于早产儿的真实数据案例展示了该方法的有效性。本文提出的方法已通过R函数实现，可作为补充材料提供。