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Modified wavelet variation for the Hermite processes

Statistics Theory 2024-03-11 v1 Probability Statistics Theory

Abstract

We define an asymptotically normal wavelet-based strongly consistent estimator for the Hurst parameter of any Hermite processes. This estimator is obtained by considering a modified wavelet variation in which coefficients are wisely chosen to be, up to negligeable remainders, independent. We use Stein-Malliavin calculus to prove that this wavelet variation satisfies a multidimensional Central Limit Theorem, with an explicit bound for the Wasserstein distance.

Keywords

Cite

@article{arxiv.2403.05140,
  title  = {Modified wavelet variation for the Hermite processes},
  author = {Laurent Loosveldt and Ciprian A. Tudor},
  journal= {arXiv preprint arXiv:2403.05140},
  year   = {2024}
}
R2 v1 2026-06-28T15:13:18.511Z