随机权函数非线性回归模型的异方差统计分析

Statistical Analysis of Heteroscedasticity in Nonlinear Regression Models with Random Weight Function

在回归分析中,随机误差是否存在方差齐性是理论与实际工作者都十分关心的问题,方差齐性假设并不总是正确的.在线性和非线性回归中关于异方差的诊断问题已有许多讨论（[1],[2],[4],[5]）.本文在韦博成（1995）讨论的加权非线性回归模型的基础上,用随机系数的方法,讨论随机权函数非线性回归模型中的异方差检验问题,得到了方差齐性检验的似然比统计量和score统计量.同时,当模型存在异方差时,本文给出了估计方差的一种方法.

The assumption of homoscedasticity is commonly concerned in regression analysis. The assumption is not always appropriate in theory and application. In linear and nonlinear regression models, there have been many testing results to discuss homoscedasticity. Based on Wei(1995), this paper deals with heteroscedasticity in nonlinear regression models with random weighted variance function. The likelihood ratio test and score test are obtained to test hypothesis of homoscedasticity. If heteroscedasticity exists, a estimating method of random weights is given.