偏t分布假设下的空间效应模型及其应用

Hierarchical Model with Spatial Effect Based on Shewed T Distribution

在非寿险索赔强度预测中,目前使用最为广泛的是广义线性模型。索赔强度的广义线性模型假设因变量服从伽马分布或逆高斯分布,且在预测项中仅能考虑协变量的线性效应。这些限制性条件都有可能影响索赔强度预测结果的准确性。本文对索赔强度的广义线性模型进行了推广:用偏T分布代替常用的伽马分布和逆高斯分布;在预测项中引入惩罚样条函数来描述连续型协变量的非线性效应;考虑索赔强度在不同地区的差异性和相邻地区的相依性。最后基于一组实际的车损险数据进行了实证研究,结果表明,本文的推广模型可以明显提高索赔强度预测模型的拟合优度。

Generalized linear models are widely used to predict the severity of non-life insurance. In generalized linear models, severity is often assumed to follow Gamma or inverse-Gaussian distribution, and covariances have linear effects on the linear predictor, which may affect the accuracy of predictions. This paper extends the present models in following aspects： Shewed T distribution is used to take place of Gamma and inverse-Gaussian distribution; penalized splines are introduced to the model to reflect the non-linear effect of continuous covariances; severity heterogeneity between distinct areas and severity dependence of adjacent areas are considered in the model.An empirical study based on a set of motor insurance loss data shows that skewed T regression models with spatial effect may significantly improve the goodness of fit.