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 provide a simulation study of the I-likelihood estimator, and we show this estimator to provide consistent performance for a variety of composite likelihood bases and interpolation methods. 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. In this application, 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.
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