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Nonparametric inference for a doubly stochastic Poisson process

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  • Utikal, Klaus J.

Abstract

Consider a doubly stochastic Poisson process whose intensity [lambda]t is given by [lambda]t=[alpha](Zt), where [alpha] is an unknown nonrandom function of another (covariate) process Zt. Only one continuous time observation of counting and covariate process is available. The function is estimated and the normalized estimator is shown to converge weakly to a Gaussian process as time approaches infinity. Confidence bands for are given. A uniformly consistent estimator of [alpha] is obtained. Consistent tests for independence from the covariate process are proposed.

Suggested Citation

  • Utikal, Klaus J., 1993. "Nonparametric inference for a doubly stochastic Poisson process," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 331-349, April.
    • Handle: RePEc:eee:spapps:v:45:y:1993:i:2:p:331-349
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    Cited by:

    1. Romain Azaïs & François Dufour & Anne Gégout-Petit, 2014. "Non-Parametric Estimation of the Conditional Distribution of the Interjumping Times for Piecewise-Deterministic Markov Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 950-969, December.

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