Montag, 09. Mai 2022, 16:45 - 17:45 iCal

ISOR Colloquium

"The Completion of Covariance Kernels"

Speaker: Victor M. Panaretos (Ecole Polytechnique Fédérale de Lausanne, Switzerland)

HS 7 OMP1 (#1.303)
Oskar-Morgenstern-Platz 1, 1090 Wien

Vortrag

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We consider the problem of positive-semidefinite continuation: extending a partially specified covariance kernel from a subdomain Ω of [0,1]^2 to a covariance kernel on the entire domain [0,1]^2. We demonstrate that for broad domain classes, a canonical completion always exists and can be explicitly constructed. We characterise all possible completions as suitable perturbations of the canonical completion, and determine necessary and sufficient conditions for a unique completion to exist. We interpret the canonical completion via the graphical model structure it induces on the associated Gaussian process. Furthermore, we show how the estimation of the canonical completion reduces to the solution of a system of linear statistical inverse problems in the space of Hilbert-Schmidt operators, and derive rates of convergence under standard source conditions. We conclude by providing extensions of our theory to more general forms of domains, and by demonstrating how our results can be used to construct covariance estimators from sample path fragments of the associated stochastic process.

Based on joint work with K.G. Waghmare, EPFL

Link to the working paper: arxiv.org/abs/2107.07350

 

The talk also can be joined online via ZOOM: univienna.zoom.us/j/66281076130

Meeting room opens at: May 9, 2022 4.30 pm Vienna

Meeting ID: 662 8107 6130

Password: 620680

Zur Webseite der Veranstaltung

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Veranstalter

Institut für Statistik und Operations Research

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Kontakt

Sabine Sobotka-Tompits, BA
Fakultät für Wirtschaftswissenschaften
Institut für Statistik und Operations Research
+43 1 4277 38631
sabine.sobotka-tompits@univie.ac.at

Erstellt am Dienstag, 19. April 2022, 09:44
Letzte Änderung am Montag, 02. Mai 2022, 14:46