Finite-sample bias-correction factors for the median absolute deviation based on the Harrell-Davis quantile estimator and its trimmed modification

TL;DR

This paper derives finite-sample bias-correction factors for the median absolute deviation using the Harrell-Davis quantile estimator and its trimmed version, improving efficiency for small samples.

Contribution

It introduces new bias-correction factors based on the Harrell-Davis estimator, enhancing the accuracy of MAD-based standard deviation estimates in small samples.

Findings

Bias-correction factors improve MAD accuracy for small samples.

Harrell-Davis based estimators outperform traditional median-based corrections.

Enhanced efficiency in standard deviation estimation for small datasets.

Abstract

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.