Time-course window estimator for ordinary differential equations linear in the parameters

Ivan Vujacic*, Itai Dattner, Javier Gonzalez, Ernst Wit

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

10 Citations (Scopus)

Abstract

In many applications obtaining ordinary differential equation descriptions of dynamic processes is scientifically important. In both, Bayesian and likelihood approaches for estimating parameters of ordinary differential equations, the speed and the convergence of the estimation procedure may crucially depend on the choice of initial values of the parameters. Extending previous work, we show in this paper how using window smoothing yields a fast estimator for systems that are linear in the parameters. Using weak assumptions on the measurement error, we prove that the proposed estimator is -consistent. The estimator does not require an initial guess for the parameters and is computationally fast and, therefore, it can serve as a good initial estimate for more efficient estimators. In simulation studies and on real data we illustrate the performance of the proposed estimator.

Original languageEnglish
Pages (from-to)1057-1070
Number of pages14
JournalStatistics and Computing
Volume25
Issue number6
DOIs
Publication statusPublished - Nov-2015

Keywords

  • Ordinary differential equation
  • Consistency
  • Step function estimator
  • Plug-in estimators
  • RECURRENT EPIDEMICS
  • SEASONAL DYNAMICS
  • MEASUREMENT ERROR
  • DISEASE DYNAMICS
  • MODELS
  • SYSTEMS
  • MEASLES
  • INFERENCE
  • KINETICS

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