Annals of the Institute of Statistical Mathematics

, Volume 49, Issue 4, pp 615–644

On Mad and Comedians

  • Michael Falk
Article

DOI: 10.1023/A:1003258024248

Cite this article as:
Falk, M. Annals of the Institute of Statistical Mathematics (1997) 49: 615. doi:10.1023/A:1003258024248

Abstract

A popular robust measure of dispersion of a random variable (rv) X is the median absolute deviation from the median med(|X - med(X)|), MAD for short, which is based on the median med(X) of X. By choosing Y = X, the MAD turns out to be a special case of the comedian med((X - med(X))(Y - med(Y))), which is a robust measure of covariance between rvs X and Y. We investigate the comedian in detail, in particular in the normal case, and establish strong consistency and asymptotic normality of empirical counterparts. This leads to a robust competitor of the coefficient of correlation as an asymptotic level-α-statistic for testing independence of X and Y. An example shows the weird fact that knowledge of the population med(X) does not necessarily pay (in the sense of asymptotic relative efficiency) when estimating the MAD.

Median absolute deviation from the medianrobust measure of correlationcomedianbreakdown pointcovariancecorrelation coefficientbivariate normal vectorsstrong consistencyasymptotic normality

Copyright information

© The Institute of Statistical Mathematics 1997

Authors and Affiliations

  • Michael Falk
    • 1
  1. 1.Mathematisch-Geographische FakultätKatholische Universität EichstättEichstättGermany