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Bootstrap Confidence Intervals in Mixtures of Discrete Distributions

Author

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  • Dimitri Karlis

    (Crest)

  • Valentin Patilea

    (Crest)

Abstract

The problem of building bootstrap con¯dence intervals for small probabilitieswith count data is considered. The true probability distribution generating the in-dependent observations is supposed to be a mixture of a given family of power seriesdistributions. The mixing distribution is estimated by nonparametric maximum like-lihood and the corresponding mixture is used for resampling. We build percentile¡tand Efron percentile bootstrap con¯dence intervals for the probabilities and we provetheir consistency in probability. The theoretical results are supported by simulationexperiments for Poisson and Geometric mixtures. We compare percentile¡t andEfron percentile bootstrap intervals with other eight bootstrap or asymptotic theorybased intervals. It appears that Efron percentile bootstrap interval outperforms thecompetitors in terms of coverage probability and length.

Suggested Citation

  • Dimitri Karlis & Valentin Patilea, 2004. "Bootstrap Confidence Intervals in Mixtures of Discrete Distributions," Working Papers 2004-06, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2004-06
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    References listed on IDEAS

    as
    1. SIMAR, Leopold, 1976. "Maximum likelihood estimation of a compound Poisson process," LIDAM Reprints CORE 271, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Theofanis Sapatinas, 1995. "Identifiability of mixtures of power-series distributions and related characterizations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 47(3), pages 447-459, September.
    3. Rudolf Beran, 1997. "Diagnosing Bootstrap Success," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 1-24, March.
    4. J.F. Walhin, & Paris, J., 1999. "Using Mixed Poisson Processes in Connection with Bonus-Malus Systems1," ASTIN Bulletin, Cambridge University Press, vol. 29(1), pages 81-99, May.
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    Cited by:

    1. Karlis, Dimitris & Patilea, Valentin, 2007. "Confidence intervals of the hazard rate function for discrete distributions using mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5388-5401, July.

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