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UID:2536@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20181029T140000
DTEND;TZID=Europe/Paris:20181029T150000
DTSTAMP:20181014T120000Z
URL:https://www.i2m.univ-amu.fr/evenements/intrinsic-wavelet-smoothing-of-
 curves-and-surfaces-of-hermitian-positive-definite-matrices/
SUMMARY: (...): Intrinsic wavelet smoothing of curves and surfaces of Hermi
 tian positive definite matrices
DESCRIPTION:: In multivariate time series analysis\, non-degenerate autocov
 ariance and spectral density matrices are necessarily Hermitian and positi
 ve definite and it is important to preserve these properties in any estima
 tion procedure. Our main contribution is the development of intrinsic wave
 let transforms and nonparametric wavelet regression for curves in the non-
 Euclidean space of Hermitian positive definite matrices. The primary focus
  is on the construction of intrinsic average-interpolation wavelet transfo
 rms in the space equipped with a natural invariant Riemannian metric. In a
 ddition\, we derive the wavelet coefficient decay and linear wavelet thres
 holding convergence rates of intrinsically smooth curves of Hermitian posi
 tive definite matrices. The intrinsic wavelet transforms are computational
 ly fast and nonlinear wavelet shrinkage or thresholding captures localized
  features\, such as cups or kinks\, in the matrix-valued curves. In the co
 ntext of nonparametric spectral estimation\, the intrinsic linear or nonli
 near wavelet spectral estimator satisfies the important property that it i
 s equivariant under a change of basis of the time series\, in contrast to 
 most existing approaches. The finite-sample performance of the intrinsic w
 avelet spectral estimator based on nonlinear tree-structured trace thresho
 lding is benchmarked against several state-of-the-art nonparametric curve 
 regression procedures in the Riemannian manifold by means of simulated tim
 e series data.This is joint work with Joris Chau (Université catholique d
 e Louvain).http://perso.uclouvain.be/rainer.vonsachs/
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