Best linear unbiased estimation and prediction in spatial models with measurement error /
Natural resources data are often both longitudinal and
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1997.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=736824281&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Natural resources data are often both longitudinal and spatial in nature. In addition, the predictors of the outcome of interest may be measured with error. For example, weather station data provide useful predictors in dendrochronology models, but the weather stations are not at the tree plot locations. Thus, the weather variables can only be predicted from the nearby weather stations. In this dissertation, we consider measurement error models where the mismeasured predictors, X, are related to the observed measurements, W, through W = []0 + []1 X + U or X = []0 + []1 W + U. Within these settings, we discuss best linear unbiased estimation and prediction and demonstrate that using E (X[]W) in place of X produces optimal results. Asymptotic inference will also be examined when the amount of information on the observed proxy of X, W, goes to infinity. Small sample comparisons between these estimators and competitors are also made. The limiting behavior of a spatial predictor as the amount of data collected increases to infinity within a fixed domain is known as infill asymptotics (Cressie (1991)). Whiting (1995) investigated the infill-asymptotic behavior of best linear unbiased predictor (BLUP) and estimated best linear unbiased predictor (EBLUP) by examining mean squared prediction error (MSPE). We first consider an extension to temporal-spatial models. Under this setting, we examine the behavior of (E)BLUPs when the amount of temporal and spatial data tends to infinity. Various configurations are studied under this setting. Additionally, we consider the use of (E)BLUPs from one spatial model as predictors in a second model. We examine the asymptotic behavior of the best linear unbiased estimator in the second model when the MSPE of (E)BLUP in the first model tends to 0. Simulation studies are presented to illustrate the proposed results. Finally, we apply these techniques to a problem in dendrecology. Data from plots of trees throughout Mississippi and Louisiana were collected through a grant from the USDA Southern Forest Experiment Station, Pineville, LA. Weather data were also provided by USDA Forest Service from 41 weather stations in Mississippi and Louisiana. A tree growth model is developed and significant variables are suggested and discussed. |
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| Item Description: | Vita. "Major Subject: Statistics". |
| Physical Description: | xiv, 111 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 92-95. |