Wavelet eigenvalue regression in high dimensions
| Autor: | Patrice Abry, B. Cooper Boniece, Gustavo Didier, Herwig Wendt |
|---|---|
| Přispěvatelé: | Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure de Lyon (ENS de Lyon)-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Department of Mathematics - University of Utah, University of Utah, Tulane University, CoMputational imagINg anD viSion (IRIT-MINDS), Institut de recherche en informatique de Toulouse (IRIT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique (Toulouse) (Toulouse INP), Université de Toulouse (UT)-Toulouse Mind & Brain Institut (TMBI), Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT), Centre National de la Recherche Scientifique (CNRS), ANR-16-CE33-0020,MULTIFRACS,Théories et méthodes multifractales multivariées pour les systèmes de grande taille - Applications à l'analyse des propriétés d'invariance d'échelle dans la dynamique de l'activité cérébrale(2016), ANR-18-CE45-0007,MUTATION,Analyse multifractale multidimensionnelle : Théorie et applications en imagerie échographique du cancer de pancréas(2018) |
| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
Operator self-similarity [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST] FOS: Mathematics Mathematics - Statistics Theory Primary: 62H25 60B20. Secondary: 42C40 60G18 Statistics Theory (math.ST) Wavelets Random matrices AMS: Primary: 62H25 60B20. Secondary: 42C40 60G18 |
| Zdroj: | Statistical Inference for Stochastic Processes Statistical Inference for Stochastic Processes, 2022, pp.1-33. ⟨10.1007/s11203-022-09279-3⟩ |
| ISSN: | 1387-0874 1572-9311 |
| DOI: | 10.1007/s11203-022-09279-3⟩ |
| Popis: | In this paper, we construct the wavelet eigenvalue regression methodology in high dimensions. We assume that possibly non-Gaussian, finite-variance $p$-variate measurements are made of a low-dimensional $r$-variate ($r \ll p$) 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. Comment: 33 pages, 3 figures. Minor revision. Companion to arXiv:2102.05761 |
| Databáze: | OpenAIRE |
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