双权数作为位置稳健估计量的效率
The Efficiency of the Biweight as a Robust Estimator of Location.
作者信息
Kafadar Karen
机构信息
National Bureau of Standards, Washington, DC 20234.
出版信息
J Res Natl Bur Stand (1977). 1983 Mar-Apr;88(2):105-116. doi: 10.6028/jres.088.006.
The biweight is one member of the family of M-estimators used to estimate location. The variance of this estimator is calculated via Monte Carlo simulation for samples of sizes 5, 10, and 20. The scale factors and tuning constants used in the definition of the biweight are varied to determine their effects on the variance. A measure of efficiency for three distributional situations (Gaussian and two stretched-tailed distributions) is determined. Using a biweight scale and a tuning constant of = 6, the biweight attains an efficiency of 98.2% for samples of size 20 from the Gaussian distribution. The minimum efficiency at 20 using the biweight scale and = 4 is 84.7%, revealing that the biweight performs well even when the underlying distibution of the samples has abnormally stretched tails.
双权函数是用于估计位置的M估计量族中的一员。该估计量的方差通过对样本量为5、10和20的样本进行蒙特卡罗模拟来计算。双权函数定义中使用的尺度因子和调整常数会发生变化，以确定它们对方差的影响。确定了三种分布情况（高斯分布和两种长尾分布）下的效率度量。使用双权函数尺度和调整常数(c = 6)时，对于来自高斯分布的样本量为20的样本，双权函数的效率达到98.2%。使用双权函数尺度和(c = 4)时，样本量为20时的最小效率为84.7%，这表明即使样本的基础分布具有异常长尾，双权函数的表现也很好。
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