A. Caponera, J. Fageot, M. Simeoni, V. M. Panaretos
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 a stationary collection of spherical random fields is sampled at a few random directions, possibly subject to measurement error. We 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. We establish representer theorems that fully characterizing 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.
Keywords: functional data analysis, measurement error, representer theorem, sparse sampling, spherical random field
Scheduled
GT06 Functional Data Analysis IV. Functional Time Series
June 9, 2022 10:10 AM
Grade Hall
