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