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Article Dans Une Revue Journal of Statistical Planning and Inference Année : 2008

Bootstrap confidence intervals in mixtures of discrete distributions

Résumé

The problem of building bootstrap confidence intervals for small probabilities with count data is addressed. The law of the independent observations is assumed to be a mixture of a given family of power series distributions. The mixing distribution is estimated by nonparametric maximum likelihood and the corresponding mixture is used for resampling. We build percentile-t and Efron percentile bootstrap confidence intervals for the probabilities and we prove their consistency in probability. The new theoretical results are supported by simulation experiments for Poisson and geometric mixtures. We compare percentile-t and Efron percentile bootstrap intervals with eight other bootstrap or asymptotic theory based intervals. It appears that Efron percentile bootstrap intervals outperform the competitors in terms of coverage probability and length

Dates et versions

hal-00377709 , version 1 (22-04-2009)

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Citer

Valentin Patilea, Dimitris Karlis. Bootstrap confidence intervals in mixtures of discrete distributions. Journal of Statistical Planning and Inference, 2008, 138 (8), pp.2313-2329. ⟨10.1016/j.jspi.2007.10.026⟩. ⟨hal-00377709⟩
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