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Jackknife methods in small -area estimation and related problems
Abstract
Small-area estimation arises in any large scale sample surveys where estimates of different characteristics of interest are needed for various subgroups of the target population. For example, the National Health and Interview Survey conducted by the National Center for Health Statistics is designed to produce national level estimates for various health related variables. However, for making health policies, reliable estimates of the same health related variables are needed for various subnational level ( e.g. states) and also for different demographic groups. The survey-based statistics for small-areas are highly variable due to small sample sizes available for the small-areas. Utilizing various administrative and census records in conjunction with the sample survey through an appropriate explicit multi-level model, it is possible to improve upon the survey estimates. Empirical Best Prediction (EBP) methods have been found to be very suitable to address small-area estimation and related problems. One advantage of EBP method is robustness—no specific distributional assumptions are required. However, one challenging problem is the development of accurate measure of uncertainty of EBP which captures all sources of variations. This issue has generated a large volume of research during the last decade. This dissertation proposes the jackknife method as a possible tool to measure uncertainty of EBP. The major part of the dissertation considers the situation when the survey estimates are modeled by the widely used Fay-Herriot model. This is a very special kind of heteroscedastic regression model where the error variance of a particular observation (i.e., estimate for a particular small-area) is composed of two parts. The first part reflects the known sampling variability that arises due to sampling, and the second part is unknown variance due to a model which connects different sources of information. Theory of the proposed jackknife method which can account for unbalancedness of the model is developed and validated through Monte Carlo simulation work. A very special case of the Fay-Herriot model which was used by many researchers is revisited and the jackknife mean squared error estimator is compared with various empirical Bayes measures of uncertainty. Interestingly, while the proposed jackknife MSE estimator satisfies standard frequentist's properties, it is also approximately same as a measure which was derived earlier from a Bayesian viewpoint. A detailed small-area analysis is presented using the data from the 1995 National Health Interview Survey. Specifically, EBP method is used to produce estimates of the proportion of individuals who had visited a doctor's office during the last twelve months for the fifty states and the District of Columbia. The analysis clearly demonstrates the utility of state level relevant administrative and census data. The proposed jackknife method is used to produce MSE estimates of the EBP. The dissertation also takes the proposed jackknife method beyond the Fay-Herriot model. In particular, a methodology is developed to implement the proposed jackknife method in mixed logistic regression models.
Subject Area
Statistics
Recommended Citation
Wan, Shu-Mei, "Jackknife methods in small -area estimation and related problems" (1999). ETD collection for University of Nebraska-Lincoln. AAI9951310.
https://digitalcommons.unl.edu/dissertations/AAI9951310