Poisson Counts, Square Root Transformation and Small Area Estimation

Malay Ghosh (), Tamal Ghosh () and Masayo Y. Hirose ()
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Malay Ghosh: University of Florida
Tamal Ghosh: University of Florida
Masayo Y. Hirose: Kyushu University

Sankhya B: The Indian Journal of Statistics, 2022, vol. 84, issue 2, No 1, 449-471

Abstract: Abstract The paper intends to serve two objectives. First, it revisits the celebrated Fay-Herriot model, but with homoscedastic known error variance. The motivation comes from an analysis of count data, in the present case, COVID-19 fatality for all counties in Florida. The Poisson model seems appropriate here, as is typical for rare events. An empirical Bayes (EB) approach is taken for estimation. However, unlike the conventional conjugate gamma or the log-normal prior for the Poisson mean, here we make a square root transformation of the original Poisson data, along with square root transformation of the corresponding mean. Proper back transformation is used to infer about the original Poisson means. The square root transformation makes the normal approximation of the transformed data more justifiable with added homoscedasticity. We obtain exact analytical formulas for the bias and mean squared error of the proposed EB estimators. In addition to illustrating our method with the COVID-19 example, we also evaluate performance of our procedure with simulated data as well.

Keywords: COVID19; Empirical Bayes; Fay-Herriot model; Random Effects Model; Stein-type shrinkage estimators.; Primary: 62C12; Secondary: 62D05 (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s13571-021-00269-8

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