Confidence intervals for median absolute deviations

TL;DR

This paper introduces interval estimators for the median absolute deviation (MAD) to enable reliable inference on dispersion measures, demonstrating their effectiveness through simulations and robustness analysis.

Contribution

It presents new interval estimators for MAD and its ratios/differences, with validation via simulations and robustness investigation using influence functions.

Findings

Coverage probabilities are close to nominal levels across various distributions.

Interval estimators perform well for single and comparative MAD analysis.

Robustness properties are confirmed through influence function analysis.

Abstract

The median absolute deviation (MAD) is a robust measure of scale that is simple to implement and easy to interpret. Motivated by this, we introduce interval estimators of the MAD to make reliable inferences for dispersion for a single population and ratios and differences of MADs for comparing two populations. Our simulation results show that the coverage probabilities of the intervals are very close to the nominal coverage for a variety of distributions. We have used partial influence functions to investigate the robustness properties of the difference and ratios of independent MADs.