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Differential equation (DE) models are widely used in many scientific fields, including engineering, physics, and biomedical sciences. The so-called “forward problem,” the problem of simulations and predictions of state variables for given parameter values in the DE models, has been extensively studied by mathematicians, physicists, engineers, and other scientists. However, the “inverse problem,” the problem of parameter estimation based on the measurements of output variables, has not been well explored using modern statistical methods, although some least squares–based approaches have been proposed and studied. In this article we propose parameter estimation methods for ordinary differential equation (ODE) models based on the local smoothing approach and a pseudo–least squares (PsLS) principle under a framework of measurement error in regression models. The asymptotic properties of the …