A Small Area Estimation under Arc-sin Transformed Area Level Model

Speaker: Masayo Hirose, Kyushu University

Title: A Small Area Estimation under Arc-sin Transformed Area Level Model

Abstract:  

An empirical best linear unbiased predictor can contribute to more efficiency, especially when the sample size within each area is not large enough to make reliable direct estimates conducted only from sample data within each area. Sometimes, it is essential to transform it properly to the original scale to conclude. However, the natural back transformation could produce a bias, especially when the sample size within an area is not large enough. In Hirose,
Ghosh, and Ghosh (2023), we found the explicit empirical Bayes estimators for arc-sin transformed data that correct biases asymptotically. Moreover, maintaining strict positivity, we explicitly obtained the second-order unbiased estimators of these mean squared prediction errors. Furthermore, we recently modified their method to handle a complex sampling design. Finally, we also applied the proposed method to poverty mapping by prefectures of Japan. These are joint works with Prof. Malay Ghosh, Dr. Tamal Ghosh (University of Florida), and Prof. Mayumi Oka (The Institute of Statistical Mathematics).