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.

中文翻译：

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广义双曲族和通过多项选择LASSO自动选择模型

我们重新审视广义双曲（GH）分布及其嵌套模型。其中包括广泛使用的参数选择，例如多元正态分布、偏斜分布、拉普拉斯和其他几个。我们还介绍了多项选择 LASSO，这是一种新颖的惩罚方法，用于在同一参数的替代约束中进行选择。分层多重选择最小绝对收缩和选择算子 (LASSO) 惩罚似然经过优化，可在 GH 系列内同时执行模型选择和推理。我们通过模拟研究和真实数据示例来说明我们的方法。本文提出的方法已在 R 函数中实现，这些函数可作为补充材料提供。