Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends. (English) Zbl 1243.62122
Summary: We develop methodology for the estimation of the functional mean and 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.
MSC:
| 62M30 | Inference from spatial processes |
| 62H20 | Measures of association (correlation, canonical correlation, etc.) |
| 85A35 | Statistical astronomy |
| 62P35 | Applications of statistics to physics |
| 65C60 | Computational problems in statistics (MSC2010) |
Software:
wmtsaReferences:
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