广义线性模型中一类推广的拟似然估计与异方差性诊断检验

本文考虑了随机设计情形下一类普通的异方差回归模型，在这个模型中，假定回归函数与方差函数之间的关系服从推广的广义非线性模型，该模型在实际中很常见，广义线性模型便是其特例，首先，我们导出了均值函数的局部加权拟似然估计，然后，用它来得到方差函数的估计，并且证明了这些估计有较好的性质，最后，建立了异方差检验统计量，文中的方法很吸引人。

On an Extended Quasi-likelihood Estimation and a Diagnostic Test for Heteroscedasticity in the Generalized linear Models

A general heteroscedastic regression model is considered in a random design setting. In this model, the relationship between the regression function and the variance function is assumed to follow an extended generalized nonlinear model which is common in practice with the generalized linear models as its special cases. Locally-weighted-quasi-likelihood estimate for the mean function is derived and is then applied to obtain an estimate of the variance function. It is also demonstrated that such estimators are with good properties. A test for heteroscedasticity is established. The methodology employed in this article is attractive.