On Mad and Comedians
- Michael Falk
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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.
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- On Mad and Comedians
Annals of the Institute of Statistical Mathematics
Volume 49, Issue 4 , pp 615-644
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- Median absolute deviation from the median
- robust measure of correlation
- breakdown point
- correlation coefficient
- bivariate normal vectors
- strong consistency
- asymptotic normality
- Industry Sectors
- Michael Falk (1)
- Author Affiliations
- 1. Mathematisch-Geographische Fakultät, Katholische Universität Eichstätt, Ostenstrasse 26-28, D-85071, Eichstätt, Germany