Parameter estimation for differential equations from noisy data arises in many fields of science and engineering. Popular methods such as nonlinear least squares and Varah's spline method are either computationally intensive or statistically inefficient or both. Ramsay et al. (2007) proposed a generalized profiling procedure. It is easily implementable and has been demonstrated to have encouraging numerical performance. However little is known about statistical properties of the procedure.;This dissertation provides a theoretical justification of the generalized profiling procedure. For a wide range of tuning parameters, the procedure is shown to be consistent. Furthermore we give sufficient conditions to obtain asymptotic efficiency. We apply the generalized profiling procedure to simulated and real data sets, and evaluate its performance with Varah's spline method and a modified profiling procedure.
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