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

TL;DR

This paper explores applying Le Cam's one-step method for efficient parameter estimation in ODE models, offering a computationally simpler alternative to traditional nonlinear least squares methods.

Contribution

It introduces a practical one-step estimation procedure starting from a nonparametric preliminary estimator, with theoretical support and demonstrated effectiveness.

Findings

The one-step estimator performs comparably to nonlinear least squares in simulations.

The method provides reliable point and interval estimates.

A data-driven approach for tuning parameter selection is proposed.

Abstract

In this paper we study application of Le Cam's one-step method to parameter estimation in ordinary differential equations models. This computationally simple technique can serve as an alternative to numerical evaluation of the popular nonlinear least squares estimator, which typically requires the use of a multi-step iterative algorithm and repetitive numerical integration of the ODE system. The one-step method starts from a preliminary $\sqrt{n}$-consistent estimator of the parameter of interest and next turns it into an asymptotic (as the sample size $n\rightarrow\infty$) 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 $\sqrt{n}$-consistent estimator that we use depends on nonparametric 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.