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October 2019 Approximating mixed Hölder functions using random samples
Nicholas F. Marshall
Ann. Appl. Probab. 29(5): 2988-3005 (October 2019). DOI: 10.1214/19-AAP1471

Abstract

Suppose $f:[0,1]^{2}\rightarrow \mathbb{R}$ is a $(c,\alpha )$-mixed Hölder function that we sample at $l$ points $X_{1},\ldots ,X_{l}$ chosen uniformly at random from the unit square. Let the location of these points and the function values $f(X_{1}),\ldots ,f(X_{l})$ be given. If $l\ge c_{1}n\log^{2}n$, then we can compute an approximation $\tilde{f}$ such that \begin{equation*}\|f-\tilde{f}\|_{L^{2}}=\mathcal{O}\big(n^{-\alpha}\log^{3/2}n\big),\end{equation*} with probability at least $1-n^{2-c_{1}}$, where the implicit constant only depends on the constants $c>0$ and $c_{1}>0$.

Citation

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Nicholas F. Marshall. "Approximating mixed Hölder functions using random samples." Ann. Appl. Probab. 29 (5) 2988 - 3005, October 2019. https://doi.org/10.1214/19-AAP1471

Information

Received: 1 October 2018; Published: October 2019
First available in Project Euclid: 18 October 2019

zbMATH: 07155064
MathSciNet: MR4019880
Digital Object Identifier: 10.1214/19-AAP1471

Subjects:
Primary: 26B35
Secondary: 42B35, 60G42

Rights: Copyright © 2019 Institute of Mathematical Statistics

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Vol.29 • No. 5 • October 2019
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