Many processes in biology, chemistry, physics, medicine, and engineering are modeled by a system of differential equations. Such a system is usually characterized via unknown parameters and estimating their ‘true’ value is thus required. In this paper we focus on the quite common systems for which the derivatives of the states may be written as sums of products of a function of the states and a function of the parameters. For such a system linear in functions of the unknown parameters we present a necessary and sufficient condition for identifiability of the parameters. We develop an estimation approach that by passes the heavy computational burden of numerical integration and avoids the estimation of system states derivatives, drawbacks from which many classic estimation methods suffer. We also suggest an experimental design for which smoothing can be circumvented. The optimal rate of the proposed estimators, i.e., their √n-consistency, is proved and simulation results illustrate their excellent finite sample performance and compare it to other estimation approaches.
|Number of pages||35|
|Journal||Electronic Journal of Statistics|
|State||Published - 19 Aug 2015|
Bibliographical notePublisher Copyright:
© 2015, Institute of Mathematical Statistics. All rights reserved.
- Local polynomials
- Non parametric regression
- Ordinary differential equation
- Plug-in estimators
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty