Mathematisches Kolloquium
Im Rahmen des Mathematischen Kolloquiums der Ruhr-Universität Bochum finden im WS 13/14 folgende Vorträge statt:
Vortrag am Mittwoch, den 29. Januar 2014, 16.15 Uhr, NA 01/99
Prof. Marc Hallin (Université Libre de Bruxelles, Princeton University)
Titel: Signal detection in high dimension: testing sphericity against spiked alternatives
Abstract:
We consider the problem of testing the null hypothesis of sphericity for
a high-dimensional covariance matrix against the alternative of a finite (unspecified)
number of symmetry-breaking directions (multispiked alternatives)
from the point of view of the asymptotic theory of statistical experiments.
The region lying below the so-called phase transition or impossibility threshold
is shown to be a contiguity region. Simple analytical expressions are
derived for the asymptotic power envelope and the asymptotic powers of existing
tests. These asymptotic powers are shown to lie very substantially
below the power envelope; some of them even trivially coincide with the size
of the test. In contrast, the asymptotic power of the likelihood ratio test is
shown to be uniformly close to the same.
Based on joint work with Marcelo Moreira, Funda¸cao Getulio Vargas, Rio
de Janeiro, and Alexei Onatski, University of Cambridge.
Onatski, A., Moreira, M. and Hallin, M. (2013). Asymptotic power of
sphericity tests for high-dimensional data. Annals of Statistics 41, 1204-
1231.
Onatski, A., Moreira, M. and Hallin, M. (2013). Signal detection in high
dimension: the multispiked case. arXiv:1210.5663.
Vortrag am Mittwoch, den 5. Februar 2014, 16.15 Uhr, Na 01/99
Prof. Dr. Paola Pozzi (Universität Duisburg-Essen)
Titel: On Willmore flow
Abstract:
In this talk I will discuss longtime existence for the elastic flow of open curves in R^n subject to fixed length and natural boundary conditions (joint work with Anna Dall'Acqua and Chun-Chi Lin).