Scaling variances, correlation and principal components with multivariate geostatistics

Persistent Link:
http://hdl.handle.net/10150/282813
Title:
Scaling variances, correlation and principal components with multivariate geostatistics
Author:
Vargas-Guzman, Jose Antonio, 1961-
Issue Date:
1998
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
A new concept of dispersion (cross) covariance has been introduced for the modeling of spatial scale dependent multivariate correlations. Such correlations between attributes depend on the spatial size of the domain and size of samples in the population and have been modeled by first time in this research. Modeled correlations have been used to introduce a new scale dependent principal component analysis (PCA) method. This method is based on computation of eigen values and vectors from dispersion covariance matrices or scale dependent correlations which can be modeled from integrals of matrix variograms. For second order stationary random functions this PCA converges for large domains to the classic PCA. A new technique for computing variograms from spatial variances have also been developed using derivatives. For completeness, a deeper analysis of the linear model of coregionalizations widely used in multivariate geostatistics has been included as well. This last part leads to a new more sophisticated model we termed "linear combinations coregionalization model." This whole research explains the relationship between different average states and the micro- state of vector random functions in the framework of geostatistics. Examples have been added to illustrate the practical application of the theory. This approach will be useful in all earth sciences and particularly in soil and environmental sciences.
Type:
text; Dissertation-Reproduction (electronic)
Keywords:
Statistics.
Degree Name:
Ph.D.
Degree Level:
doctoral
Degree Program:
Graduate College; Soil, Water and Environmental Science
Degree Grantor:
University of Arizona
Advisor:
Warrick, Arthur W.

Full metadata record

DC FieldValue Language
dc.language.isoen_USen_US
dc.titleScaling variances, correlation and principal components with multivariate geostatisticsen_US
dc.creatorVargas-Guzman, Jose Antonio, 1961-en_US
dc.contributor.authorVargas-Guzman, Jose Antonio, 1961-en_US
dc.date.issued1998en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractA new concept of dispersion (cross) covariance has been introduced for the modeling of spatial scale dependent multivariate correlations. Such correlations between attributes depend on the spatial size of the domain and size of samples in the population and have been modeled by first time in this research. Modeled correlations have been used to introduce a new scale dependent principal component analysis (PCA) method. This method is based on computation of eigen values and vectors from dispersion covariance matrices or scale dependent correlations which can be modeled from integrals of matrix variograms. For second order stationary random functions this PCA converges for large domains to the classic PCA. A new technique for computing variograms from spatial variances have also been developed using derivatives. For completeness, a deeper analysis of the linear model of coregionalizations widely used in multivariate geostatistics has been included as well. This last part leads to a new more sophisticated model we termed "linear combinations coregionalization model." This whole research explains the relationship between different average states and the micro- state of vector random functions in the framework of geostatistics. Examples have been added to illustrate the practical application of the theory. This approach will be useful in all earth sciences and particularly in soil and environmental sciences.en_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
dc.subjectStatistics.en_US
thesis.degree.namePh.D.en_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineSoil, Water and Environmental Scienceen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorWarrick, Arthur W.en_US
dc.identifier.proquest9912117en_US
dc.identifier.bibrecord.b39123613en_US
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