Nonparametric estimation of covariance and autocovariance operators
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
Other papers in the same session
J. Álvarez Liébana, W. González Manteiga, M. D. Ruiz Medina
F. D. Miranda Huaynalaya, M. D. Ruiz Medina
N. Mohammadi, V. Panaretos, L. Santoro
A. Torres Signes, M. P. Frías Bustamante, M. D. Ruiz Medina
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6/8/22
Visit Alhambra
Tomorrow, Thursday, we will visit the Alhambra. 1. At 7:00 p.m., buses will start leaving from the door of the Hotel Granada Center (in front of the door of the Faculty of Sciences) 2. Upon arrival, groups with guides will be organized. 3. There will be groups in English language. These groups will wait at the destination until the arrival of all buses. 4. After the visit to the Alhambra we will walk to the Carmen de los Mártires to have a cocktail. 5. On the way back, we can go back by bus, which will leave from the same place where they left us at the Alhambra. 6. Although the way to the Alhambra by bus seems long, it really is close to the city. We invite you, whoever wishes, to go down for a pleasant walk. 7. Do not forget to take your Alhambra ticket and your identity card or passport. The document must be the same whose number matches the ticket number you have.
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5/31/22
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5/27/22
Gala Dinner
It opens the possibility that anyone who is registered for the conference, and wants non-registered companions to attend the gala dinner, can do so by paying the price of this dinner (80 euros VAT included). This payment must be made before June 1 (inclusive). To do this, contact with [email protected]
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5/23/22
IMPORTANT WARNING
To access the Alhambra on the visit on Thursday 9, it is obligatory to present the identification document whose reference was sent to the organization (eurocongress)
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5/16/22
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