On Estimating Mean Squared Prediction Error of Small Area Estimators in Basic Area Level Model with Unknown Sampling Variance by Parametric Bootstrap

• Activity Number: 653
• Type: Contributed
• Date/Time: Thursday, August 7, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Survey Research Methods Section
• Author(s): Abhishek Nandy*+ and Snigdhansu Chatterjee
• Companies: University of Minnesota and University of Minnesota
• Keywords: Fay-Herriot ; Small Area Estimation ; Parametric Bootstrap ; Mean Squared Prediction Error

Abstract

Small Area Estimation has gained importance day by day in survey sampling for effective allocation of government funds for economic, health and social planning. The design based estimators are unreliable due to unavailability of sufficient number of observations from each small area. Measuring variability of small area estimators under basic area level models with known sampling variances is a well studied problem in literature. But estimation of small area means as well as mean square prediction error of the small area means becomes tricky when sampling variances are assumed unknown in such models because the parameters are no longer identifiable. In this article we impose some additional structure on the sampling variances in the Fay-Herriot model, and resolve the identifiability issue. We prove consistency of parameter estimates, and establish results for the mean squared prediction error, and parametric bootstrap estimates for it. We implement our method under 3 different simulation setups and one real data.