BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Talks.cam//talks.cam.ac.uk// X-WR-CALNAME:Talks.cam BEGIN:VEVENT SUMMARY:Intrinsic wavelet regression for curves and surfaces of Hermitian positive definite matrices - Rainer von Sachs (Université Catholique de L ouvain ) DTSTART:20180319T160000Z DTEND:20180319T170000Z UID:TALK102586@talks.cam.ac.uk CONTACT:INI IT DESCRIPTION:Co-author: Joris Chau (ISBA\, UC Louvain)

In multivariate time series analysis\, non-degenerate autocovaria nce and spectral density matrices are necessarily Hermitian and positive d efinite. An estimation methodology which preserves these properties is dev eloped based on intrinsic wavelet transforms being applied to nonparametri c wavelet regression for curves in the non-Euclidean space of Hermitian po sitive definite matrices. Via intrinsic average-interpolation in a Riemann ian manifold equipped with a natural invariant Riemannian metric\, we deri ve the wavelet coefficient decay and linear wavelet thresholding convergen ce rates of intrinsically smooth curves. Applying this more specifically t o nonparametric spectral density estimation\, an important property of the intrinsic linear or nonlinear wavelet spectral estimator under the invari ant Riemannian metric is that it is independent of the choice of coordina te system of the time series\, in contrast to most existing approaches. As a generalisation of this one-dimensional denoising of matrix-valued curve s in the Riemannian manifold we also present higher-dimensional intrinsic wavelet transforms\, applied in particular to time-varying spectral estima tion of non-stationary multivariate time series\, i.e. surfaces of Hermiti an positive definite matrices.

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