无重复因析试验中散度效应的ML估计  

THE ML ESTIMATOR OF DISPERSION EFFECTS IN UNREPLICATED FACTORIAL EXPERIMENTS

作　　者：王钰[1] 李济洪[1] 冯霞[1] 

机构地区：[1]山西大学计算中心,太原030006

出　　处：《系统科学与数学》2011年第7期804-816,共13页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(60873128)资助课题

摘　　要：在无重复因析试验中,若因子A,B的散度效应显著,则不论其交互效应AB的散度效应是否显著,其散度效应的现有估计常常是有偏的,从而导致其被错误地识别为显著效应.提出了散度效应的一种新的估计方法(称为ML估计),并给出了ML估计的方差的精确表达形式,证明了在一类模型中,交互效应AB的散度效应的ML估计是无偏的.最后,将ML估计与现有的常用估计进行了比较.In unreplicated factorial experiments, if the dispersion effects of factors A, B are active, the existing estimators of dispersion effects are often biased whether or not the dispersion effect of interaction factor AB is active. This results in AB be spuriously identified active factor. In this paper, we propose a new estimator of dispersion effects （called the ML estimator）, and give the exact expression of the variance of ML estimator. We prove that the ML estimator of dispersion effect of interaction factor AB is unbiased in a class of models. Finally, a comparison is given between the ML estimator and the existing and commonly used estimators.

关 键 词：无重复因析试验 散度效应 ML估计 无偏性 

分 类 号：O212.1[理学—概率论与数理统计]