Skip to Main content Skip to Navigation
Journal articles

New Weak Error bounds and expansions for Optimal Quantization

Abstract : We propose new weak error bounds and expansion in dimension one for optimal quantization-based cubature formula for different classes of functions, such that piecewise affine functions, Lipschitz convex functions or differentiable function with piecewise-defined locally Lipschitz or α-Hölder derivatives. This new results rest on the local behaviors of optimal quantizers, the L r-L s distribution mismatch problem and Zador's Theorem. This new expansion supports the definition of a Richardson-Romberg extrapolation yielding a better rate of convergence for the cubature formula. An extension of this expansion is then proposed in higher dimension for the first time. We then propose a novel variance reduction method for Monte Carlo estimators, based on one dimensional optimal quantizers.
Complete list of metadata

Cited literature [23 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-02361644
Contributor : Thibaut Montes <>
Submitted on : Friday, May 1, 2020 - 12:29:50 PM
Last modification on : Saturday, April 3, 2021 - 3:29:38 AM

File

NewErrorBound.pdf
Files produced by the author(s)

Identifiers

Citation

Vincent Lemaire, Thibaut Montes, Gilles Pagès. New Weak Error bounds and expansions for Optimal Quantization. Journal of Computational and Applied Mathematics, Elsevier, In press, 371, pp.112670. ⟨10.1016/j.cam.2019.112670⟩. ⟨hal-02361644v3⟩

Share

Metrics

Record views

160

Files downloads

352