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

摘要

In this paper we study application of Le Cam's one-step method to parameterestimation in ordinary differential equations models. This computationallysimple technique can serve as an alternative to numerical evaluation of thepopular nonlinear least squares estimator, which typically requires the use ofa multi-step iterative algorithm and repetitive numerical integration of theODE system. The one-step method starts from a preliminary $\sqrt{n}$-consistentestimator of the parameter of interest and next turns it into an asymptotic (asthe sample size $n\rightarrow\infty$) equivalent of the least squares estimatorthrough a numerically straightforward procedure. We demonstrate performance ofthe one-step estimator via extensive simulations and real data examples. Themethod enables the researcher to obtain both point and interval estimates. Thepreliminary $\sqrt{n}$-consistent estimator that we use depends onnonparametric smoothing, and we provide a data driven methodology for choosingits tuning parameter and support it by theory. An easy implementation scheme ofthe one-step method for practical use is pointed out.