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On the Construction of Unbiased Estimators for the Group Testing Problem

Author

Listed:
  • Gregory Haber

    (University of Maryland, Baltimore County)

  • Yaakov Malinovsky

    (University of Maryland, Baltimore County)

Abstract

Debiased estimation has long been an area of research in the group testing literature. This has led to the development of several estimators with the goal of bias minimization and, recently, an unbiased estimator based on sequential binomial sampling. Previous research, however, has focused heavily on the simple case where no misclassification is assumed and only one trait is to be tested. In this paper, we consider the problem of unbiased estimation in these broader areas, giving constructions of such estimators for several cases. We show that, outside of the standard case addressed previously in the literature, it is impossible to find any proper unbiased estimator, that is, an estimator giving only values in the parameter space. This is shown to hold generally under any binomial or multinomial sampling plans.

Suggested Citation

  • Gregory Haber & Yaakov Malinovsky, 2020. "On the Construction of Unbiased Estimators for the Group Testing Problem," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(1), pages 220-241, February.
    • Handle: RePEc:spr:sankha:v:82:y:2020:i:1:d:10.1007_s13171-018-0156-4
    DOI: 10.1007/s13171-018-0156-4
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    References listed on IDEAS

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    1. Joshua M. Tebbs & Christopher S. McMahan & Christopher R. Bilder, 2013. "Two-Stage Hierarchical Group Testing for Multiple Infections with Application to the Infertility Prevention Project," Biometrics, The International Biometric Society, vol. 69(4), pages 1064-1073, December.
    2. Graham Hepworth & Ray Watson, 2009. "Debiased estimation of proportions in group testing," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 58(1), pages 105-121, February.
    3. Graham Hepworth & Brad J. Biggerstaff, 2017. "Bias Correction in Estimating Proportions by Pooled Testing," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 602-614, December.
    4. Juan Ding & Wenjun Xiong, 2015. "Robust group testing for multiple traits with misclassification," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(10), pages 2115-2125, October.
    5. Shih-Hao Huang & Mong-Na Lo Huang & Kerby Shedden & Weng Kee Wong, 2017. "Optimal group testing designs for estimating prevalence with uncertain testing errors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(5), pages 1547-1563, November.
    6. Aiyi Liu & Chunling Liu & Zhiwei Zhang & Paul S. Albert, 2012. "Optimality of group testing in the presence of misclassification," Biometrika, Biometrika Trust, vol. 99(1), pages 245-251.
    7. M. Hung & William H. Swallow, 1999. "Robustness of Group Testing in the Estimation of Proportions," Biometrics, The International Biometric Society, vol. 55(1), pages 231-237, March.
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