Estimation and Testing for Spatially Distributed Curves

• Activity Number: 7
• Type: Invited
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: ASA Advisory Committee on Climate Change Policy
• Author(s): Piotr Stefan Kokoszka*+ and Sasha Gromenko
• Companies: Colorado State University and Utah State University
• Keywords: Functional data ; Spatial statistics ; Ionosphere ; Magnetic Field

Abstract

In many fields, most notably in environmental science and geosciences, data have the form of temporal curves available at unevenly distributed spatial locations. It is often of interest to combine such data to evaluate global or regional temporal trends. The research I will present is motivated by records of space physics data available at globally distributed observatories and reaching back into the 1960's. These data have been used to evaluate the hypothesis of ``global cooling'' in the ionosphere. We cast such data structures into the framework of functional data analysis, and show how the spatial dependence can be used to estimate their main parameters: the mean function and the functional principal components. These estimation techniques are then used to construct a test of independence of two families of such curves. The test is applied to assess the impact of long term changes in the internal magnetic field of the Earth on ionospheric trends. We conclude with a brief discussion of asymptotic results.