Statistica Sinica 25 (2015), 41-59

A COVARIANCE PARAMETER ESTIMATION METHOD

FOR POLAR-ORBITING SATELLITE DATA

Michael T. Horrell and Michael L. Stein

University of Chicago

Abstract: We consider the problem of estimating an unknown covariance function of a Gaussian random field for data collected by a polar-orbiting satellite. The complex and asynoptic nature of such data requires a parameter estimation method that scales well with the number of observations, can accommodate many covariance functions, and uses information throughout the full range of spatio-temporal lags present in the data. Our solution to this problem is to develop new estimating equations using composite likelihood methods as a base. We modify composite likelihood methods through the inclusion of an approximate likelihood of interpolated points in the estimating equation. The new estimating equation is denoted the I-likelihood. We apply the I-likelihood method to 30 days of ozone data occurring in a single degree latitude band collected by a polar orbiting satellite, and we compare I-likelihood methods to competing composite likelihood methods. The I-likelihood is shown capable of producing covariance parameter estimates that are equally or more statistically efficient than competing composite likelihood methods and to be more computationally scalable.

Key words and phrases: Composite likelihood, estimating equations, Gaussian random elds, Godambe information, remote sensing.