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2015 Optimal rate of direct estimators in systems of ordinary differential equations linear in functions of the parameters
Itai Dattner, Chris A. J. Klaassen
Electron. J. Statist. 9(2): 1939-1973 (2015). DOI: 10.1214/15-EJS1053


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 bypasses 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 $\sqrt{n}$-consistency, is proved and simulation results illustrate their excellent finite sample performance and compare it to other estimation approaches.


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Itai Dattner. Chris A. J. Klaassen. "Optimal rate of direct estimators in systems of ordinary differential equations linear in functions of the parameters." Electron. J. Statist. 9 (2) 1939 - 1973, 2015.


Received: 1 January 2015; Published: 2015
First available in Project Euclid: 27 August 2015

zbMATH: 1327.62120
MathSciNet: MR3391125
Digital Object Identifier: 10.1214/15-EJS1053

Primary: 62F12 , 62G05 , 62G08 , 62G20

Keywords: local polynomials , Lotka-Volterra , Nonparametric regression , ordinary differential equation , plug-in estimators

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.9 • No. 2 • 2015
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