• Corpus ID: 231879664

On high-dimensional wavelet eigenanalysis

  title={On high-dimensional wavelet eigenanalysis},
  author={Patrice Abry and B. Cooper Boniece and Gustavo Didier and Herwig Wendt},
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… 

Hurst multimodality detection based on large wavelet random matrices

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

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.



Central limit theorem for the robust log-regression wavelet estimation of the memory parameter in the Gaussian semi-parametric context

In this paper, we study robust estimators of the memory parameter d of a (possibly) non stationary Gaussian time series with generalized spectral density f. This generalized spectral density is

Asymptotic normality of wavelet estimators of the memory parameter for linear processes

Abstract.  We consider linear processes, not necessarily Gaussian, with long, short or negative memory. The memory parameter is estimated semi‐parametrically using wavelets from a sample X1,…, Xn of

On high-dimensional wavelet eigenanalysis (with a supplement on Gaussian and non-Gaussian examples)

  • arχiv (2102.05761v3),
  • 2022

Wavelet eigenvalue regression for n-variate operator fractional Brownian motion

On the Spectral Density of the Wavelet Coefficients of Long‐Memory Time Series with Application to the Log‐Regression Estimation of the Memory Parameter

Abstract.  In recent years, methods to estimate the memory parameter using wavelet analysis have gained popularity in many areas of science. Despite its widespread use, a rigorous semi‐parametric

A wavelet whittle estimator of the memory parameter of a nonstationary Gaussian time series

We consider a time series X = {X k , k ∈ Z} with memory parameter do ∈ R. This time series is either stationary or can be made stationary after differencing a finite number of times. We study the

Introduction to Random Matrices

Here I = S j (a2j 1,a2j) andI(y) is the characteristic function of the set I. In the Gaussian Unitary Ensemble (GUE) the probability that no eigenvalues lie in I is equal to �(a). Also �(a) is a

Detecting and estimating multivariate self-similar sources in highdimensional noisy mixtures, in ‘2018

  • IEEE Statistical Signal ProcessingWorkshop (SSP)’,
  • 2018

Tempered fractional Brownian motion: Wavelet estimation, modeling and testing

Wavelet estimation for operator fractional Brownian motion

Operator fractional Brownian motion (OFBM) is the natural vector-valued extension of the univariate fractional Brownian motion. Instead of a scalar parameter, the law of an OFBM scales according to a