A simplified representation of the covariance structure of axially symmetric processes on the sphere

Chunfeng Huang, Haimeng Zhang and Scott M. Robeson

Statistics & Probability Letters, 2012, vol. 82, issue 7, 1346-1351

Abstract: Spatial processes having covariance functions that depend solely on the distance between locations are known as homogeneous. Many random processes on the sphere are not homogeneous, especially in the latitudinal dimension. As a result, we study a class of statistical processes that exhibit axial symmetry, whereby their covariance function depends on differences in longitude alone. We develop a new and simplified representation for a valid axially symmetric process, reducing computational complexity considerably. In addition, we explore longitudinally reversible processes and the construction of parametric models for axially symmetric processes.

Keywords: Associated Legendre polynomials; Longitudinally reversible process; Mercer’s theorem; Spherical harmonics (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spl.2012.03.015

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