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Related Experiment Video

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Poisson Counts, Square Root Transformation and Small Area Estimation: Square Root Transformation.

Malay Ghosh1, Tamal Ghosh1, Masayo Y Hirose2

  • 1Department of Statistics, University of Florida, 223 Griffin-Floyd Hall, Gainesville, FL USA.

Sankhya. Series B (2008)
|October 18, 2021
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Summary
This summary is machine-generated.

This study introduces a novel empirical Bayes method for analyzing count data, specifically COVID-19 fatalities. The new approach uses a square root transformation for more accurate statistical modeling of rare events.

Keywords:
COVID19Empirical BayesFay-Herriot modelRandom Effects ModelStein-type shrinkage estimators.

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Area of Science:

  • Statistics
  • Biostatistics
  • Epidemiology

Background:

  • The Fay-Herriot model is a standard tool for small area estimation.
  • Analyzing count data, such as COVID-19 fatalities, often involves rare events where Poisson models are suitable.
  • Conventional empirical Bayes methods may face challenges with Poisson data due to non-conjugate priors.

Purpose of the Study:

  • To revisit the Fay-Herriot model with homoscedastic known error variance for count data analysis.
  • To propose a novel empirical Bayes (EB) estimation approach using data transformation for Poisson means.
  • To derive analytical formulas for the bias and mean squared error of the proposed EB estimators.

Main Methods:

  • A square root transformation is applied to both the Poisson data and the corresponding mean.
  • An empirical Bayes (EB) approach is used for estimation.
  • Back-transformation is employed to infer about the original Poisson means, ensuring normal approximation and homoscedasticity.

Main Results:

  • The square root transformation improves the justification for normal approximation and introduces homoscedasticity.
  • Exact analytical formulas for the bias and mean squared error of the proposed EB estimators are derived.
  • The method is illustrated using COVID-19 fatality data for Florida counties and validated with simulated data.

Conclusions:

  • The proposed EB method with square root transformation offers a statistically sound approach for analyzing count data with rare events.
  • The method provides accurate estimation and performance evaluation through derived analytical formulas.
  • This technique is applicable to various count data scenarios, including public health surveillance.