Cari colleghi
venerdì prossimo 1 aprile alle ore 15.30 avrà luogo presso il Dipartimento di Matematica di Roma Tor Vergata il seguente seminario:
------------------------------------------------------------------------------------------------------ Aula 1200, Edificio Sogene
Speaker: Alessia Caponera (EPFL)
Title: Nonparametric Estimation of Covariance and Autocovariance Operators on the Sphere
Abstract: We propose nonparametric estimators for the second-order central moments of spherical random fields within a functional data context. We consider a measurement framework where each 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 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 favours 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 fields diverges, both for the dense (increasing number of spatial samples) and sparse (bounded number of spatial samples) regimes. We moreover validate and demonstrate the practical feasibility of our estimation procedure in a simulation setting.
Based on a joint work with Julien Fageot, Matthieu Simeoni and Victor M. Panaretos
--------------------------------------------------------------------------------------------------------
Grazie per l'attenzione, Domenico Marinucci