Files
Abstract
This dissertation focuses on two different studies driven by real-world applications. For each of the studies, a fully Bayesian approach is proposed, and then relevant comparisons are done to prove the superiority of the proposed methods.
The first study focuses on providing reliable forecasts of the U.S. civilian unemployment rate. To obtain reliable forecasts, we group the states based on similarities in the time series structure or based on the region in which they are located and develop a fully Bayesian framework that borrows strength across states and uses the unemployment insurance claims data as a covariate. The Metropolis-Hastings algorithm and the Gibbs sampling method are applied to generate the posterior distributions of the relevant model parameters. Grouping states according to their similarities enables us to utilize small-area estimation to generate more accurate forecasts of UE rates for states within the same group. In terms of Mean Absolute Prediction Error (MAPE), the Bayesian framework provides more accurate forecasts than a recently developed frequentist framework called Bigtime.
In the second study, we develop a Pseudo-Bayesian small area estimation as an alternative to the empirical best linear unbiased prediction method. The empirical best linear unbiased prediction method has dominated the frequentist model-based approach to small-area estimation. This method estimates model parameters based on the marginal distribution of the data. As an alternative to this method, the observed best prediction (OBP) method estimates the parameters by minimizing an objective function that is determined by the total mean squared prediction error. Using this objective function in the well-known Fay-Herriot model, we develop a pseudo-posterior distribution for the model parameters under nearly non-informative priors. Real hospital data, median incomes of four-person households by state produced by the U.S. Census Bureau, and simulation studies show that the pseudo-Bayesian estimators (PBEs) compete favorably with the OBPs and empirical best linear unbiased predictions (EBLUPs). The PBE estimates are robust to mean misspecification and provide excellent frequentist properties. Being Bayesian by construction, they automatically avoid negative estimates of standard errors, enjoy a dual justification, and provide a desirable alternative to practitioners.
The first study focuses on providing reliable forecasts of the U.S. civilian unemployment rate. To obtain reliable forecasts, we group the states based on similarities in the time series structure or based on the region in which they are located and develop a fully Bayesian framework that borrows strength across states and uses the unemployment insurance claims data as a covariate. The Metropolis-Hastings algorithm and the Gibbs sampling method are applied to generate the posterior distributions of the relevant model parameters. Grouping states according to their similarities enables us to utilize small-area estimation to generate more accurate forecasts of UE rates for states within the same group. In terms of Mean Absolute Prediction Error (MAPE), the Bayesian framework provides more accurate forecasts than a recently developed frequentist framework called Bigtime.
In the second study, we develop a Pseudo-Bayesian small area estimation as an alternative to the empirical best linear unbiased prediction method. The empirical best linear unbiased prediction method has dominated the frequentist model-based approach to small-area estimation. This method estimates model parameters based on the marginal distribution of the data. As an alternative to this method, the observed best prediction (OBP) method estimates the parameters by minimizing an objective function that is determined by the total mean squared prediction error. Using this objective function in the well-known Fay-Herriot model, we develop a pseudo-posterior distribution for the model parameters under nearly non-informative priors. Real hospital data, median incomes of four-person households by state produced by the U.S. Census Bureau, and simulation studies show that the pseudo-Bayesian estimators (PBEs) compete favorably with the OBPs and empirical best linear unbiased predictions (EBLUPs). The PBE estimates are robust to mean misspecification and provide excellent frequentist properties. Being Bayesian by construction, they automatically avoid negative estimates of standard errors, enjoy a dual justification, and provide a desirable alternative to practitioners.