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.

翻译：绝对偏差中位数是广泛使用的统计分布的稳健度。 使用一个比例常数, 我们可以使用它作为正常情况下标准偏差的无症状一致的估测符。 对于有限的样本, 比例常数应该更正, 以便获得一个公正的估测符。 偏差校正系数取决于样本大小和中位估测符。 当我们使用传统的样本中位数时, 系数值是众所周知的, 但这种方法并不能提供最佳的统计效率 。 在本文中, 我们根据Harrell- Davis 量度估测仪及其三重修改, 给出了中位绝对偏差的偏差系数, 从而使我们能够提高标准偏差估计的统计效率 。 所获得的估计值对于少量元素的样本特别有用 。