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Nonparametric modeling of dependencies for spatial interpolation

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dc.contributor.advisor Gilbert Strang. en_US Gorsich, David John, 1968- en_US
dc.contributor.other Massachusetts Institute of Technology. Dept. of Mathematics. en_US 2005-09-27T20:03:34Z 2005-09-27T20:03:34Z 2000 en_US 2000 en_US
dc.description Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2000. en_US
dc.description Includes bibliographical references (p. 140-148). en_US
dc.description.abstract Crucial in spatial interpolation of stochastic processes is the determination of the underlying dependency of the data. The dependency can be represented by an underlying covariogram, variogram, or generalized covariogram. Estimating this function in a nonparametric way is the theme of this thesis. If the function can be found accurately, then kriging is the optimal linear interpolation technique. A nev,· technique for variogram model selection using the derivative of the empirical variogram and non-negative least squares is discussed. The eigenstructure of the spatial design matrix, the key matrix in Matheron's variogram estimator is determined. Then a nonparametric estimator of the variogram and covariogram of a spatial stochastic process is found. The optimal node selection is determined as well as conditions when the spectral coefficients can be found without a non-linear algorithm. A method of extending isotropic positive definite functions in ]Rd is determined in order to avoid a Gibbs effect on the Fourier-Bessel expansion. Finally, a nonparametric estimator of the generalized covariance is discussed. en_US
dc.description.statementofresponsibility by David John Gorsich. en_US
dc.format.extent 148 p. en_US
dc.format.extent 10416786 bytes
dc.format.extent 10416544 bytes
dc.format.mimetype application/pdf
dc.format.mimetype application/pdf
dc.language.iso eng en_US
dc.publisher Massachusetts Institute of Technology en_US
dc.rights M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission. en_US
dc.subject Mathematics. en_US
dc.title Nonparametric modeling of dependencies for spatial interpolation en_US
dc.type Thesis en_US Ph.D. en_US
dc.contributor.department Massachusetts Institute of Technology. Dept. of Mathematics. en_US
dc.identifier.oclc 47848724 en_US

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