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
Personal Website of Rainer von Sachs
The talk also can be joined online via our ZOOM MEETING
Meeting room opens at: May 25, 2022, 2.45 pm Vienna
Meeting ID: 638 6295 9776
Password: 353388