Date Available
12-3-2027
Year of Publication
2025
Document Type
Doctoral Dissertation
Degree Name
Doctor of Philosophy (PhD)
College
Arts and Sciences
Department/School/Program
Statistics
Faculty
Katherine Thompson
Faculty
Derek Young
Abstract
Small area estimation is a category of techniques that can generate more precise estimates in case with smaller samples sizes. This work proposes an extension to the Fay-Herriot model that allows for hypothesis testing and inferences to be conducted using small area estimation in designed experiments. The proposed method uses the predictors generated by the Fay-Herriot model as the response in an analysis of variance to determine if there are treatment differences and to generate confidence intervals. The proposed method is compared to a mixed model in a setting where the auxiliary data does not have influence on the response and a setting where it does. Simulation studies are used to show the performance of the proposed method. Additionally the proposed method is used to analyze real data sets. The simulation studies demonstrate that the proposed method has similar power to detect treatment differences as the mixed model in all settings. The coverage of the true parameters is closer to the nominal level under the proposed method than the mixed model in most settings. These results hold in the presence and absence of influential auxiliary data. Three different types of auxiliary data generating mechanisms are examined: a Bernoulli distribution, a discrete uniform distribution, and a standard normal distribution and the performance of the proposed method is better than or competitive with a mixed model in all settings.
Digital Object Identifier (DOI)
https://doi.org/10.13023/etd.2025.546
Recommended Citation
Stanton, Victoria, "Small Area Estimation in Agricultural Experiments" (2025). Theses and Dissertations--Statistics. 82.
https://uknowledge.uky.edu/statistics_etds/82
