Annals of Applied Statistics
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.
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.