Circulant matrices on global data analysis

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

Abstract: In this thesis, we investigate the unbiasedness of the commonly used covariance and variogram estimators when the underlying process is assumed to be stationary on the circle or axially symmetric on the sphere. We represent both estimators as a quadratic form of the observed gridded data that is associated with circulant or block circulant matrices. We then use the spectral decomposition of circulant and block circulant matrices to decompose both estimators as a linear combination of independent random variates. In particular, if the underlying process on the circle is stationary and Gaussian, both the covariance and variogram estimators are a linear combination of independent and identically distributed 21 random variates.

Additional Information

Language: English
Date: 2017
Axial symmetry, Quadratic form, Spectral decomposition, Stationarity, Unbiasedness
Symmetric matrices
Forms, Quadratic
Stochastic processes
Spatial analysis (Statistics)

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