Electronic Resource
Springer
Annals of the Institute of Statistical Mathematics
49 (1997), S. 615-644
ISSN:
1572-9052
Keywords:
Median absolute deviation from the median
;
robust measure of correlation
;
comedian
;
breakdown point
;
covariance
;
correlation coefficient
;
bivariate normal vectors
;
strong consistency
;
asymptotic normality
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1003258024248
Permalink
| Library |
Location |
Call Number |
Volume/Issue/Year |
Availability |
