# Statistical Estimates for Generalized Splines

Magnus Egerstedt; Clyde Martin

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 9, page 553-562
- ISSN: 1292-8119

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topEgerstedt, Magnus, and Martin, Clyde. "Statistical Estimates for Generalized Splines." ESAIM: Control, Optimisation and Calculus of Variations 9 (2010): 553-562. <http://eudml.org/doc/90710>.

@article{Egerstedt2010,

abstract = {
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.
},

author = {Egerstedt, Magnus, Martin, Clyde},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Optimal control; smoothing splines; linear systems; interpolation.; optimal control; interpolation},

language = {eng},

month = {3},

pages = {553-562},

publisher = {EDP Sciences},

title = {Statistical Estimates for Generalized Splines},

url = {http://eudml.org/doc/90710},

volume = {9},

year = {2010},

}

TY - JOUR

AU - Egerstedt, Magnus

AU - Martin, Clyde

TI - Statistical Estimates for Generalized Splines

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 9

SP - 553

EP - 562

AB -
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.

LA - eng

KW - Optimal control; smoothing splines; linear systems; interpolation.; optimal control; interpolation

UR - http://eudml.org/doc/90710

ER -

## References

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- S. Sun, M. Egerstedt and C. Martin, Control Theoretic Smoothing Splines. IEEE Trans. Automat. Control45 (2000) 2271-2279.
- G. Wahba, Spline Models for Observational Data. CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia (1990).
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