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Parameter estimation for discretely observed linear birth‐and‐death processes

Author

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  • A. C. Davison
  • S. Hautphenne
  • A. Kraus

Abstract

Birth‐and‐death processes are widely used to model the development of biological populations. Although they are relatively simple models, their parameters can be challenging to estimate, as the likelihood can become numerically unstable when data arise from the most common sampling schemes, such as annual population censuses. A further difficulty arises when the discrete observations are not equi‐spaced, for example, when census data are unavailable for some years. We present two approaches to estimating the birth, death, and growth rates of a discretely observed linear birth‐and‐death process: via an embedded Galton‐Watson process and by maximizing a saddlepoint approximation to the likelihood. We study asymptotic properties of the estimators, compare them on numerical examples, and apply the methodology to data on monitored populations.

Suggested Citation

  • A. C. Davison & S. Hautphenne & A. Kraus, 2021. "Parameter estimation for discretely observed linear birth‐and‐death processes," Biometrics, The International Biometric Society, vol. 77(1), pages 186-196, March.
    • Handle: RePEc:bla:biomet:v:77:y:2021:i:1:p:186-196
    DOI: 10.1111/biom.13282
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    References listed on IDEAS

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    1. Ai[dieresis]t-Sahalia, Yacine & Yu, Jialin, 2006. "Saddlepoint approximations for continuous-time Markov processes," Journal of Econometrics, Elsevier, vol. 134(2), pages 507-551, October.
    2. Xanthi Pedeli & Anthony C. Davison & Konstantinos Fokianos, 2015. "Likelihood Estimation for the INAR( p ) Model by Saddlepoint Approximation," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1229-1238, September.
    3. W. Zhang & M. V. Bravington & R. M. Fewster, 2019. "Fast likelihood‐based inference for latent count models using the saddlepoint approximation," Biometrics, The International Biometric Society, vol. 75(3), pages 723-733, September.
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