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A penalized simulated maximum likelihood method to estimate parameters for SDEs with measurement error

Author

Listed:
  • Libo Sun

    (Janssen Research and Development, LLC)

  • Chihoon Lee

    (Stevens Institute of Technology)

  • Jennifer A. Hoeting

    (Colorado State University)

Abstract

The penalized simulated maximum likelihood (PSML) approach can be used to estimate parameters for a stochastic differential equation model based on completely or partially observed discrete-time observations. The PSML uses an auxiliary variable importance sampler and parameters are estimated in a penalized maximum likelihood framework. In this paper, we extend the PSML to allow for measurement error, including unknown initial conditions. Simulation studies for two stochastic models and a real world example aimed at understanding the dynamics of chronic wasting disease illustrate that our method has favorable performance in the presence of measurement error. PSML reduces both the bias and root mean squared error as compared to existing methods. Lastly, we establish consistency and asymptotic normality for the proposed estimators.

Suggested Citation

  • Libo Sun & Chihoon Lee & Jennifer A. Hoeting, 2019. "A penalized simulated maximum likelihood method to estimate parameters for SDEs with measurement error," Computational Statistics, Springer, vol. 34(2), pages 847-863, June.
    • Handle: RePEc:spr:compst:v:34:y:2019:i:2:d:10.1007_s00180-018-0846-3
    DOI: 10.1007/s00180-018-0846-3
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    References listed on IDEAS

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