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Journal article
Wavelet eigenvalue regression in high dimensions
Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems, v 26(1)
01 Apr 2023
Abstract
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.
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Details
- Title
- Wavelet eigenvalue regression in high dimensions
- Creators
- Patrice Abry - École Normale Supérieure de LyonBenjamin Cooper Boniece - University of UtahGustavo Didier - Tulane UniversityHerwig Wendt - Institut Polytechnique de Bordeaux
- Publication Details
- Statistical inference for stochastic processes : an international journal devoted to time series analysis and the statistics of continuous time processes and dynamic systems, v 26(1)
- Publisher
- Springer Verlag
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000856509700001
- Scopus ID
- 2-s2.0-85138303654
- Other Identifier
- 991021861660804721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Statistics & Probability