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

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