[Statlist] Research Seminar in Statistics *TUESDAY, 21 JUNE 2022* GSEM, University of Geneva

[gsem-support-instituts]

Dear All,

We are pleased to invite you to our next Research Seminar.

Looking forward to seeing you,


Organized by Professor Sebastian Engelke on behalf of the Research Center for Statistics (https://www.unige.ch/gsem/en/research/institutes/rcs/)


TUESDAY, 21 JUNE 2022 at 11:15am, Uni-Mail M 5220 & ONLINE
Zoom research webinar: https://unige.zoom.us/j/92924332087?pwd=U1U1NFk4dTFCRHBMeWYrSDBQcXBiQT09
Meeting ID: 929 2433 2087
Passcode: 399192
Statistical Inference for Intrinsic Wavelet Estimators of Covariance Matrices in a log-Euclidean Manifold
(jointly with Johannes Krebs, Eichstätt, and Daniel Rademacher, Heidelberg)
Rainer von SACHS, Université catholique de Louvain, Belgium
https://perso.uclouvain.be/rainer.vonsachs/

ABSTRACT:
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.


Visit the website: https://www.unige.ch/gsem/en/research/seminars/rcs/