The Van Dantzig seminar is a nationwide series of lectures in statistics, that features renowned international and local speakers from the full breadth of the statistical sciences. The name honours David van Dantzig (1900-1959), who was the first modern statistician in the Netherlands, and professor in the “Theory of Collective Phenomena” (i.e. statistics) in Amsterdam. The seminar will convene 4 to 6 times a year at varying locations, and is financially supported by, among others, the STAR cluster and the Section Mathematical Statistics of the VVS-OR.
15.00-16.00 Thomas Verdebout (Université Libre de Bruxelles)
16.00-16.15 break
16.15-17.15 Angelika Rohde (University of Freiburg)
17.15- Drinks
Thomas Verdebout – Asymptotic power of Sobolev tests for uniformity on hyperspheres
One of the most classical problems in multivariate statistics is considered, namely, the problem of testing isotropy, or equivalently, the problem of testing uniformity on the unit hypersphere. Rather than restricting to tests that can detect specific types of alternatives only, we consider the broad class of Sobolev tests. While these tests are known to allow for omnibus testing of uniformity, their non-null behavior and consistency rates, unexpectedly, remain largely unexplored. To improve on this, we thoroughly study the local asymptotic powers of Sobolev tests under the most classical alternatives to uniformity, namely, under rotationally symmetric alternatives. We show in particular that the consistency rate of Sobolev tests does not only depend on the coefficients defining these tests but also on the derivatives of the underlying angular function at zero.
This work is in collaboration with Eduardo Garcia-Portugues and Davy Paindaveine
Angelika Rhode – Nonparametric Bootstrap of High-Dimensional Sample Covariance Matrices
We introduce a new ”$(m,mp/n)$ out of $(n,p)$”-sampling with replacement bootstrap for eigenvalue statistics of high-dimensional sample covariance matrices based on $n$ independent $p$-dimensional random vectors. In the high-dimensional scenario $p/n\rightarrow c\in (0,\infty)$, this fully nonparametric and computationally tractable bootstrap is shown to consistently reproduce the underlying spectral measure if $m/n\rightarrow 0$. If $m^2/n\rightarrow 0$, it approximates correctly the distribution of linear spectral statistics. The crucial component is a suitably defined representative subpopulation condition which is shown to be verified in a large variety of situations. Our proofs are conducted under minimal moment requirements and incorporate delicate results on non-centered quadratic forms, combinatorial trace moments estimates as well as a conditional bootstrap martingale CLT which may be of independent interest.
Everybody is cordially invited to attend.
Hanne Kekkonen and Frank van der Meulen
Recent Comments