Work

Modified wavelet variation for the Hermite processes

Year: 2025

Type: article

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.

Source: Electronic Journal of Statistics

DOI: 10.1214/25-ejs2390

Authors: Laurent Loosveldt, Ciprian A. Tudor

Institutions: University of Liège, Centre National de la Recherche Scientifique, Université de Lille, Laboratoire Paul Painlevé

Language: English

Topic: Random Matrices and Applications

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $675

Funders: Agence Nationale de la Recherche, Japan Science and Technology Agency, Core Research for Evolutional Science and Technology