变系数广义线性模型及其估计

VARYING-COEFFICIENT GENERALIZED LINEAR MODEL AND ITS ESTIMATION

本文以经典广义线性模型为基础,通过假定其中的回归变量的系数是某一度量空间中点的任意函数,提出了一类有广泛应用背景的变系数广义线性模型,增加了模型的灵活性和适应性,同时也适用于空间数据的统计分析。基于局部加权最大似然估计方法,文章讨论了变系数广义线性模型的拟合与统计推断,以及与之相关的局部权系统和其中光滑参数的确定。

The classical generalized linear model is generalized in this article by assuming the coefficients of the regressors to be arbitrary functions of the points in some metric space and a new type of regression model, called the varying-coefficient generalized linear model, is proposed. The local maximum likelihood approach is suggested to fit the model and the related issues such as determination of the local weights and the smoothing parameter therein as well as some statistical inferences are studied. The proposed model not only has higher flexibility and adaptability, but also is suitable for analysing spatial data and therefore has many applications.