不平衡二元反应的偏链回归模型及其在人寿保险中的应用
Skewed link regression models for imbalanced binary response with applications to life insurance
摘要：
对于在规定的时间段内观察到的人寿保险单的投资组合，例如，一年内，死亡通常是罕见的事件。当我们考察这些投资组合的死亡或不死亡的结果时，我们得到了一个不平衡的二元反应。流行的logistic和probit回归模型可能不适用于不平衡的二元响应，因为模型估计可能存在偏倚，如果处理不当，可能会导致严重的不利预测。在本文中，我们提出了使用偏链接回归模型（广义极值，威布尔和Frechet链接模型）作为更优越的模型来处理不平衡的二进制响应。我们采用一个完全贝叶斯方法的广义线性模型（GLM）下提出的链接功能，以帮助更好地解释高偏度。为了校准我们提出的贝叶斯模型，我们使用了一个真实的数据集的死亡索赔的经验，从人寿保险公司的投资组合。使用梅特罗波利斯-黑斯廷斯算法获得参数的贝叶斯估计值，对于贝叶斯模型选择和比较，使用了偏差信息准则（DIC）统计量。对于我们的死亡率数据集，我们发现这些倾斜链接模型比广泛使用的标准链接函数的二进制模型更优越。我们通过测量和比较总死亡人数和死亡福利来评估不同基础模型的预测能力。
英文摘要：
For a portfolio of life insurance policies observed for a stated period of time, e.g., one year, mortality is typically a rare event. When we examine the outcome of dying or not from such portfolios, we have an imbalanced binary response. The popular logistic and probit regression models can be inappropriate for imbalanced binary response as model estimates may be biased, and if not addressed properly, it can lead to serious adverse predictions. In this paper, we propose the use of skewed link regression models (Generalized Extreme Value, Weibull, and Frechet link models) as more superior models to handle imbalanced binary response. We adopt a fully Bayesian approach for the generalized linear models (GLMs) under the proposed link functions to help better explain the high skewness. To calibrate our proposed Bayesian models, we use a real dataset of death claims experience drawn from a life insurance company's portfolio. Bayesian estimates of parameters were obtained using the Metropolis-Hastings algorithm and for Bayesian model selection and comparison, the Deviance Information Criterion (DIC) statistic has been used. For our mortality dataset, we find that these skewed link models are more superior than the widely used binary models with standard link functions. We evaluate the predictive power of the different underlying models by measuring and comparing aggregated death counts and death benefits.
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