The aim of this article is to present a mixture composite regression model for claim severity modeling. Claim severity modeling poses several challenges such as multimodality, tail-heaviness, and systematic effects in data. We tackle this modeling problem by studying a mixture composite regression model for simultaneous modeling of attritional and large claims and for considering systematic effects in both the mixture components as well as the mixing probabilities. For model fitting, we present a group-fused regularization approach that allows us to select the explanatory variables that significantly impact the mixing probabilities and the different mixture components, respectively. We develop an asymptotic theory for this regularized estimation approach, and fitting is performed using a novel generalized expectation-maximization algorithm. We exemplify our approach on a real motor insurance dataset.

本文的目的是提出一种用于索赔严重性建模的混合复合回归模型。索赔严重性建模提出了一些挑战，例如数据的多模态、尾重和系统效应。我们通过研究混合复合回归模型来解决这个建模问题，该模型用于同时对损耗和大额索赔进行建模，并考虑混合成分和混合概率的系统效应。对于模型拟合，我们提出了一种组融合正则化方法，该方法允许我们选择分别显着影响混合概率和不同混合分量的解释变量。我们为这种正则化估计方法开发了渐近理论，并使用新颖的广义期望最大化算法进行拟合。