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无重复因析试验中散度效应的ML估计

王钰, 李济洪, 冯霞   

  1. 山西大学计算中心, 太原 030006
  • 收稿日期:2009-07-01 出版日期:2011-07-25 发布日期:2011-09-27

王钰, 李济洪, 冯霞. 无重复因析试验中散度效应的ML估计[J]. 系统科学与数学, 2011, 31(7): 804-816.

WANG Yu, LI Jihong, FENG Xia. THE ML ESTIMATOR OF DISPERSION EFFECTS IN  UNREPLICATED FACTORIAL EXPERIMENTS[J]. Journal of Systems Science and Mathematical Sciences, 2011, 31(7): 804-816.

THE ML ESTIMATOR OF DISPERSION EFFECTS IN  UNREPLICATED FACTORIAL EXPERIMENTS

WANG Yu, LI Jihong, FENG Xia   

  1. Computer Centre, Shanxi University, Taiyuan 030006
  • Received:2009-07-01 Online:2011-07-25 Published:2011-09-27
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.

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[1] 叶慈南. MOBVE分布参数的估计及其改进[J]. 系统科学与数学, 2001, 21(1): 107-114.
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