Data generation and estimation for axially symmertic processes on the sphere

UNCG Author/Contributor (non-UNCG co-authors, if there are any, appear on document)
Christopher D. Vanlangenberg (Creator)
The University of North Carolina at Greensboro (UNCG )
Web Site:
Haimeng Zhang

Abstract: Data from global networks and satellite sensors have been used to monitor a wide array of processes and variables, such as temperature, precipitation, etc. The modeling and analysis of global data has been extensively studied in the realm of spatial statistics in recent years. In this dissertation, we present our research in the following two areas. In the first project we consider the asymptotics of the popularly used covariance and variogram estimators based on Method of Moments (MOM) for stationary processes on the circle. Although it has been known that such estimators are asymptotically unbiased and consistent when modeling the stationary process on Euclidean spaces, our findings on the circle seem to contradict these results. Specifically, we show that the MOM covariance estimator is biased and the true covariance function may not be identifiable based on this estimator. On the other hand, the MOM variogram estimator is unbiased but inconsistent under the assumption of Gaussianity. Our second research focus is on global data generation. Our proposed parametric models generalize some of existing parametric models to capture the variation across latitudes when modeling the covariance structure of axially symmetric processes on the sphere. We demonstrate that the axially symmetric data on the sphere can be decomposed as Fourier series on circles, where the Fourier random coefficients can be expressed as circularly-symmetric complex random vectors. We develop an algorithm to generate axially symmetric data that follows the given covariance structure. All of the above theories and results are supplemented via simulations.

Additional Information

Language: English
Date: 2016
Asymptotics, Circular symmetry, Consistency, Cross covariance, Simulation, Variogram
Spatial analysis (Statistics)
Moments method (Statistics)
Analysis of covariance
Fourier series

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