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Non‐parametric Estimation of the Death Rate in Branching Diffusions

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  • R. HÖPFNER
  • M. HOFFMANN
  • E. LÖCHERBACH

Abstract

We consider finite systems of diffusing particles in with branching and immigration. Branching of particles occurs at position dependent rate. Under ergodicity assumptions, we estimate the position‐dependent branching rate based on the observation of the particle process over a time interval [0, t]. Asymptotics are taken as t → ∞. We introduce a kernel‐type procedure and discuss its asymptotic properties with the help of the local time for the particle configuration. We compute the minimax rate of convergence in squared‐error loss over a range of Hölder classes and show that our estimator is asymptotically optimal.

Suggested Citation

  • R. Höpfner & M. Hoffmann & E. Löcherbach, 2002. "Non‐parametric Estimation of the Death Rate in Branching Diffusions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(4), pages 665-692, December.
    • Handle: RePEc:bla:scjsta:v:29:y:2002:i:4:p:665-692
    DOI: 10.1111/1467-9469.00312
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    Cited by:

    1. E. Löcherbach, 2002. "Likelihood Ratio Processes for Markovian Particle Systems with Killing and Jumps," Statistical Inference for Stochastic Processes, Springer, vol. 5(2), pages 153-177, May.

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