Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends

Authors

Oleksandr Gromenko, Utah State UniversityFollow
Piotr Kokoszka, Utah State UniversityFollow
Lie Zhu, Utah State UniversityFollow
Jan Josef Sojka, Utah State UniversityFollow

Document Type

Article

Journal/Book Title/Conference

Annals of Applied Statistics

Volume

6

Issue

2

Publication Date

6-2012

First Page

669

Last Page

696

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(sk;t), t∈[0, T], observed at spatial locations s1,s2, . . . ,sN. 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.

Comments

Published in Annals of Applied Statistics. Author post print available for download through link above and at arXiv.org (arXiv:1206.6655v1).

Recommended Citation

Gromenko, O., Kokoszka, P., Zhu, L., & Sojka, J. (2012). Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends. Annals of Applied Statistics, 6(2), 669-696.