A Flexible Characterization of models for small area estimation: Theoretical developments and Applications
Year: 2011
Type: dissertation
Abstract: The demand for reliable small area estimates derived from survey data has increased greatly in recent years due to, among other things, their growing use in formulating policies and programs, allocation of government funds, regional planning, small area business decisions and other applications. Traditional area-specific (direct) estimates may not provide acceptable precision for small areas because sample sizes are seldom large enough in many small areas of interest. This makes it necessary to borrow information across related areas through indirect estimation based on models, using auxiliary information such as recent census data and current administrative data. Methods based on models are now widely accepted. The principal focus of this thesis is the development of a flexible modeling strategy in small area estimation with demonstrations and evaluations using the 1989 United States census bureau median income dataset. This dissertation is divided into two main parts, the first part deals with development of the proposed model and comparision of this model to the standard area-level Fay-Herriot model through the empirical Bayes (EB) approach. Results from these two models are compared in terms of average relative bias, average squared relative bias, average absolute bias, average squared deviation as well as the empirical mean square error. The proposed model exhibits remarkably better performance over the standard Fay-Herriot model. The second part represents our attempt to construct a hierarchical Bayes (HB) approach to estimate parameters for the proposed model, with implementation carried out by Markov chain Monte Carlo (MCMC) techniques. MCMC was implemented via the Gibbs sampling algorithm using R software package. We used several graphical tools to assess convergence and determine the length of the burn-in period. Results from the two models are compared in terms of average relative bias, average squared relative bias and average absolute bias. Our empirical results highlight the superiority of using the proposed model over the Fay-Herriot model. However, the advantage of the proposed model comes at a price since its implementation is mildly more difficult than the Fay-Herriot model.
Author: Antony Wanjoya
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W48859587