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June 2012 Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends
Oleksandr Gromenko, Piotr Kokoszka, Lie Zhu, Jan Sojka
Ann. Appl. Stat. 6(2): 669-696 (June 2012). DOI: 10.1214/11-AOAS524

Abstract

We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves $X(\mathbf{s}_{k};t)$, $t\in[0,T]$, observed at spatial locations $\mathbf{s}_{1},\mathbf{s}_{2},\ldots,\mathbf{s}_{N}$. We propose several methods, and evaluate them by means of a simulation study. Next, we develop a significance test for the correlation of two such functional spatial fields. After validating the finite sample performance of this test by means of a simulation study, we apply it to determine if there is correlation between long-term trends in the so-called critical ionospheric frequency and decadal changes in the direction of the internal magnetic field of the Earth. The test provides conclusive evidence for correlation, thus solving a long-standing space physics conjecture. This conclusion is not apparent if the spatial dependence of the curves is neglected.

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Oleksandr Gromenko. Piotr Kokoszka. Lie Zhu. Jan Sojka. "Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends." Ann. Appl. Stat. 6 (2) 669 - 696, June 2012. https://doi.org/10.1214/11-AOAS524

Information

Published: June 2012
First available in Project Euclid: 11 June 2012

zbMATH: 1243.62122
MathSciNet: MR2976487
Digital Object Identifier: 10.1214/11-AOAS524

Keywords: Functional data analysis , Ionospheric trends , spatial statistics

Rights: Copyright © 2012 Institute of Mathematical Statistics

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Vol.6 • No. 2 • June 2012
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