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Simpson, Douglas G. Chen, Huann-Sheng 2011-05-07T12:21:43Z 2011-05-07T12:21:43Z 10000-01-01 1996 "The random field model has been applied to model spatial heterogeneity for spatial data in many applications. The purpose of this dissertation is to explore statistical properties of noisy spatial data through estimation of the Gaussian random field. Large sample properties of the Maximum Likelihood Estimator (MLE) of an Onrstein-Uhlenbeck process model with measurement error are studied. The effect caused by adding measurement error, or ""nugget,"" is revealed by the fixed region asymptotics of the MLE. The kriging predictor with estimated covariance is discussed under such models. An extension to regression models is proposed and its asymptotic properties are examined." The Gaussian random field is characterized by its corresponding covariance function. By means of constructing the multi-dimensional covariance function from one-dimensional covariance functions, some spatial process models applicable to both spatial and regression data are proposed. The estimation of covariance functions for these models is studied. Large sample theory for some estimators is provided. Made available in DSpace on 2011-05-07T12:21:43Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9702476.pdf: 3000944 bytes, checksum: 45de7776fbf10d62a24581839fc5dad7 (MD5) Previous issue date: 1996 Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:40:05Z Item is restricted indefinitely. Restriction data tranferred 2014-07-01T11:17:04-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission ETDs are only available to UIUC Users without author permission U of I Only 9780591087352 AAI9702476 (UMI)AAI9702476 http://hdl.handle.net/2142/19883 eng Copyright 1996 Chen, Huann-Sheng Biology, Biostatistics Statistics Estimation in random field models for noisy spatial data text Biology, Biostatistics Statistics Biology, Biostatistics Statistics University of Illinois at Urbana-Champaign Dissertation Ph.D.