Accelerated least squares estimation for systems of ordinary differential equations Article Swipe
We study the problem of parameter estimation for a system of ordinary differential equations based on noisy observations on the solution of the system. A classical estimation approach to this problem is the least squares method. Owing to a highly nonlinear character of the least squares criterion function and the need to employ repetitive numerical integration of the system, the latter method becomes computationally intense for most realistic systems. We propose the accelerated (ACCEL) least squares method, which starts from a preliminary \sqrt{n}-consistent estimator of the parameter of interest and next through a Newton-Raphson type step turns it into an asymptotically equivalent estimator to the least squares estimator. Additional computational burden of this step is negligible. We demonstrate excellent practical performance of the ACCEL least squares approach via simulations and real data examples. The method enables the researcher to obtain both point and interval estimates.
