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• W2092016490 abstract "We consider the average caseL∞-approximation of functions fromCr([0, 1]) with respect to ther-fold Wiener measure. An approximation is based onnfunction evaluations in the presence of Gaussian noise with varianceσ2>0. We show that the n th minimal average error is of ordern−(2r+1)/(4r+4) ln1/2 n, and that it can be attained either by the piecewise polynomial approximation using repetitive observations, or by the smoothing spline approximation using non-repetitive observations. This completes the already known results forLq-approximation withq<∞ andσ⩾0, and forL∞-approximation withσ=0." @default.
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• W2092016490 creator A5072564885 @default.
• W2092016490 date "1998-06-01" @default.
• W2092016490 modified "2023-09-27" @default.
• W2092016490 title "Average CaseL∞-Approximation in the Presence of Gaussian Noise" @default.
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• W2092016490 doi "https://doi.org/10.1006/jath.1998.3175" @default.
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