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Confidence regions for the intensity function of a cyclic Poisson process

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Abstract

A classical approach to constructing simultaneous confidence intervals (i.e., confidence bands or regions) for a function is via establishing a limiting process of the appropriately normalized difference between the function and its empirical estimator. In the present paper we depart from this approach and construct confidence bands for the intensity function of a cyclic Poisson process via extreme value type asymptotic results for the appropriately normalized supremum of the difference between the intensity function and its empirical estimator.

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Authors and Affiliations

  1. Centre for Mathematics and Computer Science, P. O. Box 94079, Amsterdam, 1090 GB, The Netherlands

    Roelof Helmers

  2. School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, 2006, Australia

    Qiying Wang

  3. Department of Statistical and Actuarial Sciences, University of Western Ontario, London, ON, Canada, N6A 5B7

    Ričardas Zitikis

Authors
  1. Roelof Helmers
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  2. Qiying Wang
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  3. Ričardas Zitikis
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Correspondence to Ričardas Zitikis.

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Helmers, R., Wang, Q. & Zitikis, R. Confidence regions for the intensity function of a cyclic Poisson process. Stat Inference Stoch Process 12, 21–36 (2009). https://doi.org/10.1007/s11203-007-9016-x

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  • DOI: https://doi.org/10.1007/s11203-007-9016-x

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