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

Ivan Vujačić, Itai Dattner, Javier González, Ernst Wit

Research output: Contribution to journalArticlepeer-review

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 $$\sqrt{n}$$n-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
StatePublished - 30 Nov 2015

Bibliographical note

Funding Information:
The authors are very grateful to the reviewers and to the Associate Editor for their very useful comments, which enabled us to greatly improve the manuscript. Vujačić acknowledges financial support through the JoinEUsee project scholarship. Wit and González acknowledge financial support through the NWO SBC-EMA-435065 project grant. The authors would like to thank Amit Huppert (Gertner Institute for Epidemiology & Health Policy Research, Israel) for useful discussions concerning the real data example. We also thank Prof. H.G. Bock (Heidelberg University) and Dr. A. Abbruzzo (University of Palermo) for providing important references for this work.

Publisher Copyright:
© 2014, Springer Science+Business Media New York.

Keywords

  • Consistency
  • Ordinary differential equation
  • Plug-in estimators
  • Step function estimator

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics

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