统计学与应用    Vol.4 No.2 (June 2015)

基于改进的中位数绝对偏差稳健尺度估计
Robust Scale Estimation Based on the Improved Median Absolute Deviations

作者: 杨苹莉 ：中国矿业大学(北京)，北京;

关键词: 尺度估计； 稳健性； 得分函数； Scale Estimation； Robustness； Score Function

摘要:
本文基于Smirnor-Shevlyakov在2014年针对位置参数已知为0的稳健尺度估计(即改进的中位数绝对偏差FQn)，提出了位置参数未知时的稳健尺度估计(称之为广义中位数绝对偏差GMAD)。数据分析表明：FQn在位置参数未知时不稳健，但GMAD估计在位置参数为0以及未知时均稳健。

Abstract: Robust scale estimation with unknown location parameters which is called general median absolute deviations (GMAD) was proposed based on a robust scale estimation with location parameters of 0 (improved median absolute deviations FQn) given by Smirnor-Shevlyakov in 2014. The data analysis showed that FQn loses robustness when location parameters are unknown, but GMAD is robust when location parameters are zero or unknown.

文章引用: 杨苹莉 (2015) 基于改进的中位数绝对偏差稳健尺度估计。 统计学与应用， 4， 94-102. doi: 10.12677/SA.2015.42011

参考文献

[1] 茆诗松, 等 (2006) 高等数理统计. 高等教育出版社, 北京, 147-156.

[2] Huber, P.J. (1981) Robust statistics. John Wiley & Sons, Inc., New York.

[3] Rousseeuw, P. and Croux, C. (1993) Alternatives to the median absolute deviation. Journal of the American Statistical Association, 88, 1273-1283.

[4] Smirnov, P.O. and Shevlyakov, G.L. (2014) Fast highly efficient and robust one-step M-estimators of scale based on Qn. Computational Statistics & Data Analysis, 78, 153-158.

[5] Smirnov, P. and Shevlyakov, G. (2010) On approximation of the Qn-estimate of scale by fast M-estimates. In: Book of Abstracts: International Conference on Robust Statistics, ICORS 2010, Prague, Czech Republic, 94-95.

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