论文标题
基于Harrell-Davis分位数及其修剪修饰的中值绝对偏差的有限样本偏差校正因子
Finite-sample bias-correction factors for the median absolute deviation based on the Harrell-Davis quantile estimator and its trimmed modification
论文作者
论文摘要
中值绝对偏差是一种广泛使用的统计分散量。使用比例常数，我们可以将其用作正态性下标准偏差的渐近一致估计器。对于有限样品，应校正尺度常数，以获得无偏的估计器。偏差校正因子取决于样本量和中值估计器。当我们使用传统样本中位数时，因子值是众所周知的，但是这种方法不能提供最佳的统计效率。在本文中，我们介绍了基于Harrell-Davis分位数估计器及其修剪修饰的中值绝对偏差的偏差校正因子，这使我们能够实现标准偏差估计的更好的统计效率。获得的估计量对于少量元素的样品特别有用。
The median absolute deviation is a widely used robust measure of statistical dispersion. Using a scale constant, we can use it as an asymptotically consistent estimator for the standard deviation under normality. For finite samples, the scale constant should be corrected in order to obtain an unbiased estimator. The bias-correction factor depends on the sample size and the median estimator. When we use the traditional sample median, the factor values are well known, but this approach does not provide optimal statistical efficiency. In this paper, we present the bias-correction factors for the median absolute deviation based on the Harrell-Davis quantile estimator and its trimmed modification which allow us to achieve better statistical efficiency of the standard deviation estimations. The obtained estimators are especially useful for samples with a small number of elements.
