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 tornparameter estimation in ordinary differential equation models. Thisrncomputationally simple technique can serve as an alternative tornnumerical evaluation of the popular non-linear least squares estimator,rnwhich typically requires the use of a multistep iterative algorithmrnand repetitive numerical integration of the ordinary differentialrnequation system. The one-step method starts from a preliminaryrnn~(1/2)-consistent estimator of the parameter of interest and next turns itrninto an asymptotic (as the sample size n → ∞) equivalent of the leastrnsquares estimator through a numerically straightforward procedure.rnWe demonstrate performance of the one-step estimator via extensivernsimulations and real data examples. The method enables thernresearcher to obtain both point and interval estimates. The preliminaryrnn~(1/2)-consistent estimator that we use depends on non-parametricrnsmoothing, and we provide a data-driven methodology for choosingrnits tuning parameter and support it by theory. An easy implementationrnscheme of the one-step method for practical use is pointed out.