Application of one-step method to parameter estimation in ODE models

Itai Dattner, Shota Gugushvili

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we study application of Le Cam's one-step method to parameter estimation in ordinary differential equation models. This computationally simple technique can serve as an alternative to numerical evaluation of the popular non-linear least squares estimator, which typically requires the use of a multistep iterative algorithm and repetitive numerical integration of the ordinary differential equation system. The one-step method starts from a preliminary n-consistent estimator of the parameter of interest and next turns it into an asymptotic (as the sample size n→∞) equivalent of the least squares estimator through a numerically straightforward procedure. We demonstrate performance of the one-step estimator via extensive simulations and real data examples. The method enables the researcher to obtain both point and interval estimates. The preliminary n-consistent estimator that we use depends on non-parametric smoothing, and we provide a data-driven methodology for choosing its tuning parameter and support it by theory. An easy implementation scheme of the one-step method for practical use is pointed out.

Original languageEnglish
Pages (from-to)126-156
Number of pages31
JournalStatistica Neerlandica
Volume72
Issue number2
DOIs
StatePublished - May 2018

Bibliographical note

Funding Information:
The first author was supported by the Israeli Science Foundation grant number 387/15 and by a grant from the GIF, the German-Israeli Foundation for Scientific Research and Development, number I-2390-304.6/2015. The second author was supported by the European Research Council under ERC grant agreement 320637.

Funding Information:
The idea of using the one-step Le Cam method in the context of parameter inference for ODEs was proposed to us by C. A. J. Klaassen (University of Amsterdam), who was also involved in early stages of the present research. We would like to thank him for most stimulating discussions and helpful remarks. We would also like to thank the referees for their suggestions that improved the presentation in this paper. The first author was supported by the Israeli Science Foundation grant number 387/15 and by a grant from the GIF, the German-Israeli Foundation for Scientific Research and Development, number I-2390-304.6/2015. The second author was supported by the European Research Council under ERC grant agreement 320637.

Publisher Copyright:
© 2018 The Authors. Statistica Neerlandica published by John Wiley & Sons Ltd on behalf of VVS.

Keywords

  • 62G20
  • Levenberg–Marquardt algorithm
  • Secondary: 62G08
  • integral estimator
  • non-linear least squares
  • one-step estimator.AMS 2000 classifications: Primary: 62F12
  • ordinary differential equations
  • smooth and match estimator

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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