The Generalized Linear Model (GLM) for the Gamma distribution (glmGamma) is widely used in modeling continuous, non-negative and positive-skewed data, such as insurance claims and survival data. However, model selection for GLM depends on AIC/BIC criteria, which is computationally impractical for even a moderate number of variables. In this paper, we develop variable selection for glmGamma using elastic net regularization (glmGammaNet), for which we provide an algorithm and implementation. The glmGammaNet model is more challening than other more common GLMs as the likelihood function has no global quadratic upper bound, and we develop an efficient accelerated proximal gradient algorithm using a local model. We report simulation study results and discuss the choice of regularization parameter. The method is implemented in the R package glmGammaNet.

翻译：Gamma 分布( glmGamma) 的通用线性模型(GLM) 被广泛用于模拟连续、非负和正偏向的数据,如保险索赔和生存数据。 但是, GLM 的模型选择取决于 AIC/BIC 标准, 即使是数量中小的变量, 也计算不切实际。 在本文中, 我们使用弹性网正规化( glmGammaNet) 开发 glmGammam 变量选择, 我们为此提供了一种算法和实施。 glmGammaNet 模型比其他更常见的GLMs 更具有震撼动性, 因为概率函数没有全球四边形上界, 我们使用本地模型开发高效加速的准梯度算法。 我们报告模拟研究结果并讨论正规化参数的选择。 该方法在 R 包 GlmGammaNet 中实施。