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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Annals of the Institute of Statistical Mathematics 49 (1997), S. 615-644 
    ISSN: 1572-9052
    Schlagwort(e): Median absolute deviation from the median ; robust measure of correlation ; comedian ; breakdown point ; covariance ; correlation coefficient ; bivariate normal vectors ; strong consistency ; asymptotic normality
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: 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.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    New York, NY [u.a.] : Wiley-Blackwell
    Journal of Computational Chemistry 17 (1996), S. 409-417 
    ISSN: 0192-8651
    Schlagwort(e): Chemistry ; Theoretical, Physical and Computational Chemistry
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Chemie und Pharmazie , Informatik
    Notizen: We have developed a molecular modeling procedure to determine the relative configuration of a chiral molecule from nuclear magnetic resonance (NMR) data. Our procedure uses constrained molecular mechanics, and the constraints are interproton distances derived from the experimental nuclear Overhauser enhancement (NOE) data. The main feature is a period of high-temperature dynamics in which frequent inversions occur at most chiral sites. This allows the distance constraints to guide the molecule into configurations consistent with the NOE data. For molecules with complex ring systems, high-temperature dynamics alone may fail to invert certain chiral centers with sufficient frequency. We have countered this by allowing as an option additional inversions of selected chiral centers. The procedure tested successfully on organic molecules of known stereochemistry, with 5 to 17 chiral centers, provided that the number of available constraints was at least twice the number of chiral centers. The procedure is tolerant of large errors in the estimated interproton distances and is reasonably rapid. For a series of sugars, the time required increases less than quadratically with the number of atoms. © 1996 by John Wiley & Sons, Inc.
    Zusätzliches Material: 2 Ill.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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