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Hannu Oja, Tampere U. Print
Friday, 02 October 2009, 14:30 - 15:30

Invariant coordinate selection (ICS) and multivariate location, scatter, skewness and kurtosis.

Hannu Oja, University of Tampere

ABSTRACT: The classical measures of univariate location and scale are the mean and variance (or standard deviation), and the classical skewness and kurtosis measures are given by standardized third and fourth moments, respectively. We extend the classical measures to the multivariate case, and show how they can be used to construct an invariant coordinate system. Asymptotical results for multivariate skewness and kurtosis measures (and invariant coordinates) are outlined. It is also shown that any two multivariate location measures (vectors) and any two multivariate scatter measures (matrices) may be used in a similar way. The theory is illustrated with several examples.

 

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