Mittwoch, 25. Mai 2022, 15:00 - 16:00 iCal

ISOR Colloquium

"Statistical inference for intrinsic wavelet estimators of covariance matrices in a log-Euclidean manifold"

Speaker: Rainer von Sachs (Université catholique de Louvain, Belgium)

HS 17 OMP1 (#2.314)
Oskar-Morgenstern-Platz 1, 1090 Wien


In this talk we treat statistical inference for an intrinsic wavelet estimator of curves of symmetric positive definite (SPD) matrices in a log-Euclidean manifold. Examples for these arise in Diffusion Tensor Imaging or related medical imaging problems as well as in computer vision and for neuroscience problems.

Our proposed wavelet (kernel) estimator preserves positive-definiteness and enjoys permutation-equivariance, which is particularly relevant for covariance matrices. Our second-generation wavelet estimator is based on average-interpolation and allows the same powerful properties, including fast algorithms, known from nonparametric curve estimation with wavelets in standard Euclidean set-ups.

The core of our work is the proposition of confidence sets for our high-level wavelet estimator in a non-Euclidean geometry. We derive asymptotic normality of this estimator, including explicit expressions of its asymptotic variance. This opens the door for constructing asymptotic confidence regions which we compare with our proposed bootstrap scheme for inference. Detailed numerical simulations confirm the appropriateness of our suggested inference schemes.

Joint work with Johannes Krebs, Eichstätt, and Daniel Rademacher, Heidelberg


The talk also can be joined online via ZOOM:

Meeting room opens at: May 25, 2022 2.45 pm Vienna

Meeting ID: 638 6295 9776

Password: 353388

Zur Webseite der Veranstaltung


Institut für Statistik und Operations Research


Sabine Sobotka-Tompits, BA
Fakultät für Wirtschaftswissenschaften
Institut für Statistik und Operations Research
+43 1 4277 38631