Modified wavelet variation for the Hermite processes

Hermits process; Multiple Wiener-Itô integrals; Wavelet analysis; Stein-Malliavin calculus; Asymptotic normality; Central limit theorem; Self-similarity; Hurst parameter estimation; Strong consistency

Abstract :

[en] 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.

Disciplines :

Mathematics

Author, co-author :

Loosveldt, Laurent ; Université de Liège - ULiège > Département de mathématique > Probabilités - Analyse stochastique

Tudor, Ciprian A.

Language :

English

Title :

Modified wavelet variation for the Hermite processes

Publication date :

13 May 2025

Journal title :

Electronic Journal of Statistics

eISSN :

1935-7524

Publisher :

Institute of Mathematical Statistics, United States - Ohio

Volume :

19 (2025)

Pages :

2411–2455

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 11 March 2024

Statistics

Number of views

150 (10 by ULiège)

Number of downloads

58 (5 by ULiège)

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Bibliography

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