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Large deviation probabilities in estimation of Poisson random measures

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  • Florens, Danielle
  • Pham, Huyên

Abstract

We consider the parametric estimation problem of intensity measure of a Poisson random measure. We prove large deviation principles for Poisson random measures and an implicit contraction principle. These results are applied to provide a large deviation principle for a maximum likelihood estimator in a parametric statistical model and to explicitly identify the rate function.

Suggested Citation

  • Florens, Danielle & Pham, Huyên, 1998. "Large deviation probabilities in estimation of Poisson random measures," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 117-139, August.
    • Handle: RePEc:eee:spapps:v:76:y:1998:i:1:p:117-139
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    References listed on IDEAS

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    1. de Acosta, A., 1994. "Large deviations for vector-valued Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 51(1), pages 75-115, June.
    2. Hutton, James E. & Nelson, Paul I., 1984. "Interchanging the order of differentiation and stochastic integration," Stochastic Processes and their Applications, Elsevier, vol. 18(2), pages 371-377, November.
    3. Sørensen, Michael, 1990. "On quasi likelihood for semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 35(2), pages 331-346, August.
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    Cited by:

    1. Macci, Claudio & Pacchiarotti, Barbara, 2017. "Large deviations for estimators of the parameters of a neuronal response latency model," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 65-75.
    2. Léonard, C., 2000. "Large deviations for Poisson random measures and processes with independent increments," Stochastic Processes and their Applications, Elsevier, vol. 85(1), pages 93-121, January.
    3. Florens, Danielle & Pham, Huyên, 1999. "Large deviation principle in nonparametric estimation of marked point processes," Statistics & Probability Letters, Elsevier, vol. 41(4), pages 383-388, February.

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