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On local asymptotic normality for birth and death on a flow

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  • Höpfner, R.
  • Löcherbach, E.

Abstract

We consider statistical models for birth and death on a flow and prove local asymptotic normality as the observation time approaches infinity; as a consequence, we know how to characterize asymptotically efficient estimators for the unknown parameter. We construct a sequence of minimum distance estimators based on observed death positions which is strongly consistent and asymptotically normal, and improve it to get an efficient estimator for a parameter present in the death rate function.

Suggested Citation

  • Höpfner, R. & Löcherbach, E., 1999. "On local asymptotic normality for birth and death on a flow," Stochastic Processes and their Applications, Elsevier, vol. 83(1), pages 61-77, September.
    • Handle: RePEc:eee:spapps:v:83:y:1999:i:1:p:61-77
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    References listed on IDEAS

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    1. Phelan, Michael J., 1994. "A quasi likelihood for integral data on birth and death on flows," Stochastic Processes and their Applications, Elsevier, vol. 53(2), pages 379-392, October.
    2. Cremers, Heinz & Kadelka, Dieter, 1986. "On weak convergence of integral functionals of stochastic processes with applications to processes taking paths in LEP," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 305-317, February.
    3. Phelan, Michael J., 1997. "Approach to stationarity for birth and death on flows," Stochastic Processes and their Applications, Elsevier, vol. 66(2), pages 183-207, March.
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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.
    2. R. HÖpfner & E. LÖcherbach, 1998. "Birth and Death on a Flow: Local Time and Estimation of a Position‐Dependent Death Rate," Statistical Inference for Stochastic Processes, Springer, vol. 1(3), pages 225-243, October.

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