On Modeling Heteroskedasticity: The Student's t and Elliptical Linear Regression Models
提出一种利用数据图信息建模异方差的新方法，将正态/线性/同方差模型扩展至非正态/线性/异方差族，适用于处理厚尾、个体异质性和非线性依赖等异方差来源。
This paper proposes a new approach to modeling heteroskedastidty which enables the modeler to utilize information conveyed by data plots in making informed decisions on the form and structure of heteroskedasticity. It extends the well-known normal/linear/homoskedastic models to a family of non-normal/linear/heteroskedastic models. The non-normality is kept within the bounds of the elliptically symmetric family of multivariate distributions (and in particular the Student's t distribution) that lead to several forms of heteroskedasticity, including quadratic and exponential functions of the conditioning variables. The choice of the latter family is motivated by the fact that it enables us to model some of the main sources of heteroskedasticity: “thicktails,” individual heterogeneity, and nonlinear dependence. A common feature of the proposed class of regression models is that the weak exogeneity assumption is inappropriate. The estimation of these models, without the weak exogeneity assumption, is discussed, and the results are illustrated by using cross-section data on charitable contributions.