Date: 2013-11-29

Time: 15:30-16:30

Location: Concordia MB-2.270

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.

Speaker

Marc Hallin is a Professor of Statistics at the European Center for Advanced Research in Economics and Statistics, Université Libre de Bruxelles, Belgium. He is currently visiting the ORFE Department at Princeton.