具有结构变化的非线性回归模型的阶段异方差检验  

Testing for Phased Heteroscedasticity in Nonlinear Models With Structural Change

作　　者：李勇[1,2] 林金官[1] 韦博成[1] 

机构地区：[1]东南大学数学系,南京江苏210096 [2]香港中文大学统计系,中国香港

出　　处：《数学进展》2007年第3期327-338,共12页Advances in Mathematics（China）

基　　金：国家自然科学基金(No.10671032).

摘　　要：对于具有结构变化的非线性回归模型,两阶段的随机误差同时具有方差齐性是一个基本假设,但是该假设未必正确．本文研究该模型阶段异方差的检验问题．首先探讨了两阶段异方差的同时检验,然后构造了两阶段异方差的两个单个检验,分别得到了同时检验和单个检验的score统计量以及相应的调整形式．然后应用得到的检验统计量分析了南澳大利亚洋葱数据的阶段异方差性(Ratkowsky,1983),并用AIC,SBC进行模型比较,得到的结果与检验结果非常吻合．最后,用Monte Carlo模拟方法研究了统计量的检验功效．In nonlinear regression model with structural change, it is a standard assumption that the random errors of two phases both have constant variances. However, this assumption is not necessarily appropriate. This paper devotes to studying the tests for phased variance heterogeneity in these models. We first discuss the simultaneous test for variance heterogeneity of their two phases, then construct two individual tests for variance heterogeneity in each phase. Three score test statistics and their adjusted forms are obtained. Furthermore, we apply these statistics to analysize the phased variance heterogeneity of the data set of south Austrilian onion （Ratkowsky （1983））, then use the AIC and SBC crition to make a model selection and get the same result with the score test method. At last, the properties of those statistics obtained are investigated through Monte Carlo simulation method.

关 键 词：具有结构变化的非线性回归模型 阶段异方差 SCORE检验 调整的score检验 AIC SBC MONTE CARLO模拟 

分 类 号：O212.2[理学—概率论与数理统计]