## 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. |

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