Statistical estimates for generalized splines
ESAIM: Control, Optimisation and Calculus of Variations, Volume 9  (2003), p. 553-562

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.

DOI : https://doi.org/10.1051/cocv:2003026
Classification:  93-xx
Keywords: optimal control, smoothing splines, linear systems, interpolation
@article{COCV_2003__9__553_0,
     author = {Egerstedt, Magnus and Martin, Clyde},
     title = {Statistical estimates for generalized splines},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     publisher = {EDP-Sciences},
     volume = {9},
     year = {2003},
     pages = {553-562},
     doi = {10.1051/cocv:2003026},
     zbl = {1070.41003},
     mrnumber = {1998714},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2003__9__553_0}
}
Egerstedt, Magnus; Martin, Clyde. Statistical estimates for generalized splines. ESAIM: Control, Optimisation and Calculus of Variations, Volume 9 (2003) , pp. 553-562. doi : 10.1051/cocv:2003026. http://www.numdam.org/item/COCV_2003__9__553_0/

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