## The Annals of Applied Statistics

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

#### 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.

#### Article information

Source
Ann. Appl. Stat. Volume 6, Number 2 (2012), 669-696.

Dates
First available in Project Euclid: 11 June 2012

http://projecteuclid.org/euclid.aoas/1339419612

Digital Object Identifier
doi:10.1214/11-AOAS524

Mathematical Reviews number (MathSciNet)
MR2976487

Zentralblatt MATH identifier
1243.62122

#### Citation

Gromenko, Oleksandr; Kokoszka, Piotr; Zhu, Lie; Sojka, Jan. Estimation and testing for spatially indexed curves with application to ionospheric and magnetic field trends. Ann. Appl. Stat. 6 (2012), no. 2, 669--696. doi:10.1214/11-AOAS524. http://projecteuclid.org/euclid.aoas/1339419612.

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