# On high-dimensional wavelet eigenanalysis

@inproceedings{Abry2021OnHW, title={On high-dimensional wavelet eigenanalysis}, author={Patrice Abry and B. Cooper Boniece and Gustavo Didier and Herwig Wendt}, year={2021} }

In this paper, we characterize the asymptotic and large scale behavior of the eigenvalues of wavelet random matrices 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. We show that the r largest eigenvalues of the…

## 2 Citations

### Hurst multimodality detection based on large wavelet random matrices

- Computer Science2022 30th European Signal Processing Conference (EUSIPCO)
- 2022

A statistical methodology for detecting multimodality in the distribution of Hurst exponents in high-dimensional fractal systems based on the analysis of the distri-bution of the log-eigenvalues of large wavelet random matrices.

### Wavelet eigenvalue regression in high dimensions

- Mathematics, Computer ScienceStatistical Inference for Stochastic Processes
- 2022

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.

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