Electronic Journal of Statistics

A Universal Kriging predictor for spatially dependent functional data of a Hilbert Space

Alessandra Menafoglio, Piercesare Secchi, and Matilde Dalla Rosa

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Abstract

We address the problem of predicting spatially dependent functional data belonging to a Hilbert space, with a Functional Data Analysis approach. Having defined new global measures of spatial variability for functional random processes, we derive a Universal Kriging predictor for functional data. Consistently with the new established theoretical results, we develop a two-step procedure for predicting georeferenced functional data: first model selection and estimation of the spatial mean (drift), then Universal Kriging prediction on the basis of the identified model. The proposed methodology is applied to daily mean temperatures curves recorded in the Maritimes Provinces of Canada.

Article information

Source
Electron. J. Statist., Volume 7 (2013), 2209-2240.

Dates
Received: October 2012
First available in Project Euclid: 19 September 2013

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1379596770

Digital Object Identifier
doi:10.1214/13-EJS843

Mathematical Reviews number (MathSciNet)
MR3108813

Zentralblatt MATH identifier
1293.62120

Subjects
Primary: 62H11: Directional data; spatial statistics
Secondary: 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11] 62M30: Spatial processes

Keywords
Functional data analysis Sobolev metrics spatial prediction variogram

Citation

Menafoglio, Alessandra; Secchi, Piercesare; Dalla Rosa, Matilde. A Universal Kriging predictor for spatially dependent functional data of a Hilbert Space. Electron. J. Statist. 7 (2013), 2209--2240. doi:10.1214/13-EJS843. https://projecteuclid.org/euclid.ejs/1379596770


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