非参数的广义转换异方差模型(英文)

Modeling risk using nonparametric generalized transformed heteroscedasticity models

在风险管理中,费用的平均值E[Y|X]是一个关键参数.预测平均费用的主要困难在于费用数据是严重偏态且异方差.目前常用的方法有转换模型及广义线性模型方法,这两个方法独立被研究,没有任何交叉,它们部分地克服了数据的偏态性及异方差性质.本文提出了一个新的非参数模型,它不要求给定转换函数、联系函数、方差函数及误差分布函数.现有的转换模型及广义线性模型都只是这个模型的特例,该模型可以在一个相当广泛的范围内提供一个最好的选择.更重要的是本文用一个非常简单的方法估计感兴趣的参数,估计过程中不涉及未知的转换函数、联系函数、方差函数及误差分布函数,因此估计的有效性将被极大提高.理论研究显示该估计是渐进正态的.模拟的数据研究显示估计有很好的小样本举止.

In this paper we develop a new non-parametric generalized transformation heteroscedasticity regression model to predict the expected value of an outcome of a patient with given covariates, E [ Y ｜ X ], when the distribution of the outcome is highly skewed with a heteroscedastic variance. In the new model, we allow the variance function, the link function, the transformation function and the error distribution function, all to be unknown. The existing GLM and the transformation models are just special cases of the new model, the proposed model can provide a best choice in a much broader class of models than the combination of the existing models. Based on the model, we proposed a method to estimate E [ Y ｜ X ] and the regression parameters. Unlike the traditional method, we directly estimate E [ Y ｜ X ] and the regression parameters without involving the variance function, the link function, the transformation function and the error distribution function, as a result, the efficiency of the estimators will be improved. Our simulations show that the proposed nonparametric method is robust with limited loss of efficiency. Finally, the proposed estimators for regression parameters and E [ Y ｜ X ] are asymptotically normal with simple variance estimator for E [ Y ｜ X ].