Wavelet eigenvalue regression in high dimensions - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Statistical Inference for Stochastic Processes Année : 2022

Wavelet eigenvalue regression in high dimensions

Résumé

In this paper, we construct the wavelet eigenvalue regression methodology (Abry and Didier in J Multivar Anal 168:75–104, 2018a; in Bernoulli 24(2):895–928, 2018b) in high dimensions. We assume that possibly non-Gaussian, finite-variance p-variate measurements are made of a low-dimensional r-variate (r≪p) fractional stochastic process with non-canonical scaling coordinates and in the presence of additive high-dimensional noise. The measurements are correlated both time-wise and between rows. Building upon the asymptotic and large scale properties of wavelet random matrices in high dimensions, the wavelet eigenvalue regression is shown to be consistent and, under additional assumptions, asymptotically Gaussian in the estimation of the fractal structure of the system. We further construct a consistent estimator of the effective dimension r of the system that significantly increases the robustness of the methodology. The estimation performance over finite samples is studied by means of simulations.
Fichier principal
Vignette du fichier
2108.03770.pdf (2.55 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03850430 , version 1 (14-11-2022)

Identifiants

Citer

Patrice Abry, Benjamin Cooper Boniece, Gustavo Didier, Herwig Wendt. Wavelet eigenvalue regression in high dimensions. Statistical Inference for Stochastic Processes, 2022, pp.1-33. ⟨10.1007/s11203-022-09279-3⟩. ⟨hal-03850430⟩
51 Consultations
55 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More