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  • 1
    Electronic Resource
    Electronic Resource
    On Mad and Comedians (1997)
    Springer
    Annals of the Institute of Statistical Mathematics 49 (1997), S. 615-644 
    Details
    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
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  • 2
    Electronic Resource
    Electronic Resource
    LAN of extreme order statistics (1995)
    Springer
    Annals of the Institute of Statistical Mathematics 47 (1995), S. 693-717 
    Details
    ISSN: 1572-9052
    Keywords: Extreme order statistics ; local asymptotic normality ; central sequence ; generalized Pareto distributions ; asymptotic sufficiency ; optimal tests
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Consider an iid sampleZ 1,...,Z n with common distribution functionF on the real line, whose upper tail belongs to a parametric family {F β: β∈⊝}. We establish local asymptotic normality (LAN) of the loglikelihood process pertaining to the vector(Z n−i+1∶n ) i=1 k of the upperk=k(n)→ n→∞∞ order statistics in the sample, if the family {F β:β∈⊝} is in a neighborhood of the family of generalized Pareto distributions. It turns out that, except in one particular location case, thekth-largest order statisticZ n−k+1∶n is the central sequence generating LAN. This implies thatZ n−k+1∶n is asymptotically sufficient and that asymptotically optimal tests for the underlying parameter β can be based on the single order statisticZ n−k+1∶n . The rate at whichZ n−k+1∶n becomes asymptotically sufficient is however quite poor.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01856542
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