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The Poisson Compound Decision Problem Revisited

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  • Lawrence D. Brown
  • Eitan Greenshtein
  • Ya'acov Ritov

Abstract

The compound decision problem for a vector of independent Poisson random variables with possibly different means has a half-century-old solution. However, it appears that the classical solution needs smoothing adjustment. We discuss three such adjustments. We also present another approach that first transforms the problem into the normal compound decision problem. A simulation study shows the effectiveness of the procedures in improving the performance over that of the classical procedure. A real data example is also provided. The procedures depend on a smoothness parameter that can be selected using a nonstandard cross-validation step, which is of independent interest. Finally, we mention some asymptotic results.

Suggested Citation

  • Lawrence D. Brown & Eitan Greenshtein & Ya'acov Ritov, 2013. "The Poisson Compound Decision Problem Revisited," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 741-749, June.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:502:p:741-749
    DOI: 10.1080/01621459.2013.771582
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    Cited by:

    1. Park, Junyong, 2018. "Simultaneous estimation based on empirical likelihood and general maximum likelihood estimation," Computational Statistics & Data Analysis, Elsevier, vol. 117(C), pages 19-31.
    2. Albouy, David & Christensen, Peter & Sarmiento-Barbieri, Ignacio, 2020. "Unlocking amenities: Estimating public good complementarity," Journal of Public Economics, Elsevier, vol. 182(C).
    3. Stoltenberg, Emil Aas & Hjort, Nils Lid, 2020. "Multivariate estimation of Poisson parameters," Journal of Multivariate Analysis, Elsevier, vol. 175(C).

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