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Bias-reduced maximum likelihood estimation of the zero-inflated Poisson distribution

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  • Jacob Schwartz
  • David E. Giles

Abstract

We investigate the small-sample quality of the maximum likelihood estimators (MLE) of the parameters of a zero-inflated Poisson distribution (ZIP). The finite-sample bias of the MLE is determined to O(n−1) using an analytic bias-reduction methodology based on the work of Cox and Snell (1968) and Cordeiro and Klein (1994). Monte Carlo simulations show that the MLEs have very small percentage biases for this distribution, but the analytic bias-reduction methods essentially eliminate the bias without adversely affecting the mean-squared errors of the estimators. The analytic adjustment compares favorably with the parametric bootstrap bias-corrected estimator, in terms of bias reduction itself, as well as with respect to mean-squared error and Pitman’s nearness measure.

Suggested Citation

  • Jacob Schwartz & David E. Giles, 2016. "Bias-reduced maximum likelihood estimation of the zero-inflated Poisson distribution," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(2), pages 465-478, January.
    • Handle: RePEc:taf:lstaxx:v:45:y:2016:i:2:p:465-478
    DOI: 10.1080/03610926.2013.824590
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    Cited by:

    1. Costa-Font, Joan & Jimenez-Martin, Sergi & Vilaplana, Cristina, 2018. "Does long-term care subsidization reduce hospital admissions and utilization?," Journal of Health Economics, Elsevier, vol. 58(C), pages 43-66.
    2. David E. Giles, 2012. "A Note on Improved Estimation for the Topp-Leone Distribution," Econometrics Working Papers 1203, Department of Economics, University of Victoria.
    3. Joseph Reath & Jianping Dong & Min Wang, 2018. "Improved parameter estimation of the log-logistic distribution with applications," Computational Statistics, Springer, vol. 33(1), pages 339-356, March.
    4. Ryan T. Godwin & David E. Giles, 2017. "Analytic Bias Correction for Maximum Likelihood Estimators When the Bias Function is Non-Constant," Econometrics Working Papers 1702, Department of Economics, University of Victoria.
    5. Mahdi Teimouri, 2022. "bccp: an R package for life-testing and survival analysis," Computational Statistics, Springer, vol. 37(1), pages 469-489, March.

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