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We consider the problem of parameter estimation for a system of ordinarydifferential equations from noisy observations on a solution of the system. Incase the system is nonlinear, as it typically is in practical applications, ananalytic solution to it usually does not exist. Consequently, straightforwardestimation methods like the ordinary least squares method depend on repetitiveuse of numerical integration in order to determine the solution of the systemfor each of the parameter values considered, and to find subsequently theparameter estimate that minimises the objective function. This induces a hugecomputational load to such estimation methods. We study the consistency of analternative estimator that is defined as a minimiser of an appropriate distancebetween a nonparametrically estimated derivative of the solution and theright-hand side of the system applied to a nonparametrically estimatedsolution. This smooth and match estimator (SME) bypasses numerical integrationaltogether and reduces the amount of computational time drastically compared toordinary least squares. Moreover, we show that under suitable regularityconditions this smooth and match estimation procedure leads to a$\sqrt{n}$-consistent estimator of the parameter of interest.

$\sqrt{n}$-consistent parameter estimation for systems of ordinary differential equations: bypassing numerical integration via smoothing