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Resampling methods in small area estimation and disease mapping
This dissertation concerns model selection as well as resampling methods in small-area estimation and disease mapping problems. ^ The first two chapters examine the Cp criterion, a popular method of model selection, when applied to linear regression models and more complex models like the nested error regression model. We consider a jackknife estimate of the variance of the Cp statistic and propose a stepwise model selection procedure which takes into account the variance of the Cp criterion. The Cp criterion is shown to perform poorly when applied to more complex models like nested error regression model. A transformation is used which improves the performance of the Cp statistic. ^ In a typical large-scale sample survey, the sampling design is developed to produce reliable survey estimates of various target population characteristics. However, for fund allocation and public policy making, it is often essential to produce similar estimates for various subgroups of the target population. For example, the Nebraska Department of Health and Human Services is interested in producing estimates of illicit drug users for the state, all the 93 counties of Nebraska, and various domains obtained by cross-classifying various demographic groups such as age, gender and race. ^ A standard design-based estimator for a particular small-area of interest is not well suited since it tends to produce large variance due to small sample size available from the individual small-area. Different types of indirect estimation techniques have been proposed in the literature. They generally combine various relevant census and administrative records with the sample survey data using either implicit or explicit models. ^ The second half of the dissertation deals with small area estimation, in particular as applied to the disease mapping problem—a problem of great interest to epidemiologists, medical demographers, and biostatisticians. We consider multi-level Poisson modeling with covariates and address the important problem associated with measures of accuracy of empirical Bayes estimators by a hybrid of parametric bootstrap and delta methods. The proposed measure accurately captures all sources of uncertainty in approximating the MSE of the proposed empirical Bayes estimator. This dissertation makes a significant advancement of the parametric bootstrap theory put forward by earlier researchers who considered normality-based methods. Various methods are implemented using a data set obtained from the Department of Preventive and Societal Medicine at the University of Nebraska Medical Center. ^ In chapter 5, Small area estimation methods are also used to analyze data from the United States Postal Service. ^
Meza, Jane Louise, "Resampling methods in small area estimation and disease mapping" (2000). ETD collection for University of Nebraska - Lincoln. AAI9977005.