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Estimation of Poisson mean with under‐reported counts: a double sampling approach

Author

Listed:
  • Debjit Sengupta
  • Tathagata Banerjee
  • Surupa Roy

Abstract

Count data arising in various fields of applications are often under‐reported. Ignoring undercount naturally leads to biased estimators and inaccurate confidence intervals. In the presence of undercount, in this paper, we develop likelihood‐based methodologies for estimation of mean using validation data. The asymptotic distributions of the competing estimators of the mean are derived. The impact of ignoring undercount on the coverage and length of the confidence intervals is investigated using extensive numerical studies. Finally an analysis of heat mortality data is presented.

Suggested Citation

  • Debjit Sengupta & Tathagata Banerjee & Surupa Roy, 2020. "Estimation of Poisson mean with under‐reported counts: a double sampling approach," Australian & New Zealand Journal of Statistics, Australian Statistical Publishing Association Inc., vol. 62(4), pages 508-535, December.
    • Handle: RePEc:bla:anzsta:v:62:y:2020:i:4:p:508-535
    DOI: 10.1111/anzs.12308
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    References listed on IDEAS

    as
    1. Peter Fader & Bruce Hardie, 2000. "A note on modelling underreported Poisson counts," Journal of Applied Statistics, Taylor & Francis Journals, vol. 27(8), pages 953-964.
    2. Wai-Yin Poon & Hai-Bin Wang, 2010. "Bayesian Analysis of Multivariate Probit Models with Surrogate Outcome Data," Psychometrika, Springer;The Psychometric Society, vol. 75(3), pages 498-520, September.
    3. Zhijian Chen & Grace Y. Yi & Changbao Wu, 2011. "Marginal methods for correlated binary data with misclassified responses," Biometrika, Biometrika Trust, vol. 98(3), pages 647-662.
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