Optimal rate of direct estimators in systems of ordinary differential equations linear in functions of the parameters

By Itai Dattner, Chris A. J. Klaassen. 2013

59 citations recorded by the source corpus.

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 √n-consistency, is proved and simulation results illustrate their excellent finite sample performance and compare it to other estimation approaches.

Subfields: Control and Systems Engineering, Statistics and Probability

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Niels Richard Hansen
2. Frederik Vissing Mikkelsen
3. Daniela M. Witten
4. Ali Shojaie
5. Shizhe Chen

In Statistics and Probability

1. Ali Shojaie
2. Niels Richard Hansen
3. Daniela M. Witten
4. Shizhe Chen
5. Frederik Vissing Mikkelsen

Citations in the corpus

• Network Reconstruction From High-Dimensional Ordinary Differential Equations (2016, methodology): “…et al., 2002; Ramsay et al., 2007; Brunel, 2008; Cao and Zhao, 2008; Liang and Wu, 2008; Cao et al., 2011; Lu et al., 2011; Gugushvili and Klaassen, 2012; Brunel et al., 2014; Hall and Ma, 2014; Henderson and Michai-lidis, 2014; Wu et al., 2014; Dattner and Klaassen, 2015; Zhang et al., 2015).”
• Learning Large Scale Ordinary Differential Equation Systems (2017, methodology): “The data set was replicated 250 times and for each of them we applied a Gaussian kernel smoother with a range of bandwidths followed by the method proposed by Dattner & Klaassen (2015) to obtain parameter estimates.”