| ON WEIGHTED RANDOMLY TRIMMED MEANS |
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| 作者姓名： | Ting WANG Yong LI Hengjian CUI |
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| 作者单位： | [1]School of Mathematical Sciences, Statistical Data Analysis Laboratory, Beijing Normal University, Beijing 100875, China; Institute of Information Sciences and Technology, Massey University, Private Bag 11222, Palmerston North, New Zealand. [2]School of Mathematical Sciences, Statistical Data Analysis Laboratory, Beijing Normal University, Beijing 100875, China. |
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| 基金项目： | This research is supported by the National Natural Science Foundation of China （Grant No. 10371012, 10231030,and 40574020）. |
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| 摘 要： | A class of robust location estimators called weighted randomly trimmed means are introduced and not only their consistency and asymptotic normality are proved, but their influence functions, asymptotic variances and breakdown points are also derived. They possess the same breakdown points as the median, and some of them own higher asymptotic relative efficiencies at the heavy-tailed distributions than some other well-known location estimators; whereas the trimmed means, Winsorized means and Huber＇s M-estimator possess higher asymptotic relative efficiencies at the light-tailed distributions, in which Huber＇s M-estimator is the most robust.
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| 关 键 词： | 加权随机平衡均数 渐进正态性 分布函数 崩溃点 |
| 修稿时间： | 2005-12-282006-10-13 |
On Weighted Randomly Trimmed Means |
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| Ting WANG Yong LI Hengjian CUI.ON WEIGHTED RANDOMLY TRIMMED MEANS[J].Journal of Systems Science and Complexity,2007,20(1):47-65. |
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| Authors: | Ting Wang Yong Li Hengjian Cui |
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| Institution: | (1) School of Mathematical Sciences, Statistical Data Analysis Laboratory, Beijing Normal University, Beijing, 100875, China;(2) Institute of Information Sciences and Technology, Massey University, Private Bag 11222, Palmerston North, New Zealand |
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| Abstract: | A class of robust location estimators called weighted randomly trimmed means are introduced and not only their consistency
and asymptotic normality are proved, but their influence functions, asymptotic variances and breakdown points are also derived.
They possess the same breakdown points as the median, and some of them own higher asymptotic relative efficiencies at the
heavy-tailed distributions than some other well-known location estimators; whereas the trimmed means, Winsorized means and
Huber’s M-estimator possess higher asymptotic relative efficiencies at the light-tailed distributions, in which Huber’s M-estimator
is the most robust.
This research is supported by the National Natural Science Foundation of China (Grant No. 10371012, 10231030, and 40574020). |
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| Keywords: | Asymptotic normality asymptotic relative efficiency breakdown points consistency influence function |
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