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A concentration approach to sensitivity studies in statistical estimation problems

机译：统计估计问题中的敏感性研究的集中方法

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摘要

It is shown that the concept of concentration is of potential interest in the sensitivity study of some parameters and related estimators. Basic ideas are introduced for a real parameter θ ＞ 0 together with graphical representations using Lorenz curves of concentration. Examples based on the mean, standard deviation and variance are provided for some classical distributions. This concentration approach is also discussed in relation with influence functions. Special emphasis is given to the average concentration of an estimator which provides a sensitivity measure allowing one to compare several estimators of the same parameter. Properties of this measure are investigated through simulation studies and its practical interest is illustrated by examples based on the trimmed mean and the Winsorized variance.
机译：结果表明，浓度概念在某些参数和相关估计量的敏感性研究中具有潜在的意义。介绍了有关实参θ＞ 0的基本思想以及使用浓度Lorenz曲线的图形表示。为一些经典分布提供了基于均值，标准差和方差的示例。还结合影响函数讨论了这种集中方法。特别强调了估算器的平均浓度，它提供了一种敏感度度量，允许人们比较同一参数的多个估算器。通过模拟研究来研究此度量的属性，并通过基于修剪均值和Winsorized方差的示例说明其实际用途。

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