Statistical Estimates for Generalized Splines
Magnus Egerstedt, Clyde Martin (2010)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper it is shown that the generalized smoothing spline obtained by solving an optimal control problem for a linear control system converges to a deterministic curve even when the data points are perturbed by random noise. We furthermore show that such a spline acts as a filter for white noise. Examples are constructed that support the practical usefulness of the method as well as gives some hints as to the speed of convergence.