Functional Estimation of Anisotropic Covariance and Autocovariance Operators on the Sphere

07.10.2022 11:15 – 12:15

RESEARCH CENTER FOR STATISTICS SEMINAR / 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 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 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.

Lieu

Bâtiment: Uni Mail

ONLINE & in Uni Mail

Boulevard du Pont-d'Arve 40
1205 Geneva

Room M 5220, 5th floor

entrée libre