[Statlist] Research Seminar in Statistics *FRIDAY, 7 OCTOBER 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/)


FRIDAY, 7 OCTOBER 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

Functional Estimation of Anisotropic Covariance and Autocovariance Operators on the Sphere
(jointly with Julien Fageot, Matthieu Simeoni, and Victor M. Panaretos)
Alessia CAPONERA, EPFL, Switzerland
https://people.epfl.ch/alessia.caponera/?lang=en

ABSTRACT:
We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distributed collection of spherical random fields is sampled at a few random directions, possibly subject to measurement error. The collection of random fields could be i.i.d. or serially dependent. Though similar setups have already been explored for random functions defined on the unit interval, the nonparametric estimators proposed in the literature often rely on local polynomials, which do not readily extend to the (product) spherical setting. We therefore formulate our estimation procedure as a variational problem involving a generalized Tikhonov regularization term. The latter favors smooth covariance/autocovariance functions, where the smoothness is specified by means of suitable Sobolev-like pseudo-differential operators. Using the machinery of reproducing kernel Hilbert spaces, we establish representer theorems that fully characterize the form of our estimators. We determine their uniform rates of convergence as the number of random fields diverges, both for the dense (increasing number of spatial samples) and sparse (bounded number of spatial samples) regimes. We moreover demonstrate the computational feasibility of our estimation procedure in a simulation setting.


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