Exact distributions of the median absolute deviation and it's application to test of the equality of two variances

摘要

In reliability engineering, robust methods of estimation and tests play important roles. The MAD (Median Absolute Deviation) is one of the well-known robust estimators of scale. Various papers have appeared over the years dealing with the asymptotic properties of the MAD and these applications. However, surprisingly, the exact distribution of the MAD has never been derived. We then derive the exact distribution of the MAD for any continuous distribution. We furthermore propose a robust test of the equality of two variances using the MAD. Numerical studies are conducted to investigate the properties of the proposed test in terms of robustness.