15. ÖMG-Kongress
Jahrestagung der Deutschen Mathematikervereinigung

16. bis 22. September 2001 in Wien

Sektion 12 - Wahrscheinlichkeitstheorie, Statistik
Montag, 17. September 2001, 17.30, Hörsaal 7


Smooth tests of fit and multivariate skewness and kurtosis

Bernhard Klar, Universität Karlsruhe


Smooth tests are frequently used for testing the goodness of fit of a parametric family of distributions. One reason for the popularity of the smooth tests are the diagnostic properties commonly attributed to them. In recent years, however, it has been realized that these tests are non-diagnostic when used conventionally. In this talk, we examine how the smooth test statistics must be rescaled in order to obtain procedures having diagnostic properties at least for large sample sizes.

Further, we use the results in [1] to treat the limit laws of different measures of multivariate skewness and kurtosis which are related to components of Neyman's smooth test of fit for multivariate normality. Special emphasis is given to the case that the underlying distribution is elliptically symmetric.

[1] KLAR, B. (2000): Diagnostic smooth tests of fit. Metrika 52, 237-252.

E-Mail: Bernhard.Klar@math.uni-karlsruhe.de
Homepage: mspcdip.mathematik.uni-karlsruhe.de/personen/klar/klar.html

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