具有AR(1)误差的线性随机效应模型中方差齐性和自相关性的检验  

Testing of Homogeneity for Variance and Autocorrelation in Linear Models with AR(1) Errors and Random Effects

作　　者：刘应安[1] 韦博成[1] 林金官[1] 

机构地区：[1]东南大学数学系

出　　处：《应用概率统计》2004年第1期27-36,共10页Chinese Journal of Applied Probability and Statistics

基　　金：国家自然科学基金(10371016);东南大学博士后基金.

摘　　要：在回归分析中,方差齐性是一个很基本的假设.本文对具有AR(1)误差的线性随机效应模型,研究了方差齐性和自相关性的检验问题.我们分别讨论了随机误差异方差、随机效应异方差、多元异方差以及自相关性的检验问题,并用score检验方法给出了三种方差齐性和自相关性的检验统计量.随机模拟的结果表明,当样本容量较大时,检验的功效较好.本文还给出一个数值例子说明检验方法的实用性.另外,模型的结果也可以推广到非线性情形.It is a standard assumption for regression models that the error terms all have equal variances. It is of considerable interest to the test of homogeneity for variance in many practical studies. In this paper, we discuss the test of homogeneity for variance and autocorrelation in linear models with AR(1) errors and random-effects. We study the tests of autocorrelation and heteroscedasticity for random errors and random-effects, respectively. Three test statistics based on the score test are proposed. The simulation study shows that test is good as sample size is large. A practical example is given to illustrate our test method. Our results can also be extended to nonlinear models with AR(1) errors and random effects.

关 键 词：AR(1)误差 线性随机效应模型 方差齐性 自相关性 SCORE检验 

分 类 号：O212.1[理学—概率论与数理统计]