Existence test of moments: Application to Multifractal Analysis

The scope of this paper is to present a wavelet-based technique aimed at determining the range of existence for the moments of arbitrary random variables. Our work relies on the characterization of the local Hölder regularity of the characteristic function, as an indicator of the interval bounds under interest. Our motivation stems from multifractal analysis of processes.

Simple statistical analysis of wavelet-based multifractal spectrum estimation

The multifractal spectrum characterizes the scaling and singularity structures of signals and proves useful in numerous applications, from network traffic analysis to turbulence. Of great concern is the estimation of the spectrum from a finite data record. In this paper, we derive asymptotic expressions for the bias and variance of a wavelet-based estimator for a fractional Brownian motion (fBm) process. Numerous numerical simulations demonstrate the accuracy and utility of our results.

Pseudo Affine Wigner Distributions

In this paper, we define a new set of tools for time-varying spectral analysis: the pseudo affine Wigner distributions. Based on the affine Wigner distributions of J. and P. Bertrand, these new time-frequency distributions support efficient online operation at the same computational cost as the continuous wavelet transform. Moreover, they take advantage of the proportional bandwidth smoothing inherent in the sliding structure of their implementation to suppress cumbersome interference components. To formalize their place within the echelon of the affine class of time-frequency distributions, we extend the definition of this class and introduce other natural generators. 1. INTRODUCTION Time-frequency distributions (TFDs), which analyze signals in terms of joint time and frequency coordinates, have proven useful in a wide variety of fields. Most TFDs of current interest belong to either (or both of) Cohen's class [1] or the affine class [2, 3]. While Cohen's class TFDs are covariant to ..

EDICS Number SP–2.3.1 Time-Frequency Signal Analysis

We introduce a new method for the time-scale analysis of non-stationary signals. Our work leverages the success of the “time-frequency distribution series / cross-term deleted representations ” into the time-scale domain to match wide-band signals that are better modeled in terms of time shifts and scale changes than in terms of time and frequency shifts. Using a wavelet decomposition and the Bertrand time-scale distribution, we locally balance linearity and bilinearity in order to provide good resolution while suppressing troublesome interference components. The theory of frames provides a unifying perspective for cross-term deleted representations in general

Diverging moments and parameter estimation

Journal PaperHeavy tailed distributions enjoy increased popularity and become more readily applicable as the arsenal of analytical and numerical tools grows. They play key roles in modeling approaches in networking, finance, hydrology to name but a few. The tail parameter is of central importance as it governs both the existence of moments of positive order and the thickness of the tails of the distribution. Some of the best known tail estimators such as Koutrouvelis and Hill are either parametric or show lack in robustness or accuracy. This paper develops a shift and scale invariant, non-parametric estimator for both, upper and lower bounds for orders with finite moments. The estimator builds on the equivalence between tail behavior and the regularity of the characteristic function at the origin and achieves its goal by deriving a simplified wavelet analysis which is particularly suited to characteristic functions.Defense Advanced Research Projects AgencyNational Science Foundatio

A Simple Statistical Analysis of

The multifractal spectrum characterizes the scaling and singularity structures of signals and proves useful in numerous applications, from network traffic analysis to turbulence. Of great concern is the estimation of the spectrum from a finite data record. In this paper, we derive asymptotic expressions for the bias and variance of a wavelet-based estimator for a fractional Brownian motion (fBm) process. Numerous numerical simulations demonstrate the accuracy and utility of our results

Hybrid Linear / Bilinear Time-Scale Analysis

We introduce a new method for the time-scale analysis of non-stationary signals. Our work leverages the success of the "time-frequency distribution series / cross-term deleted representations" into the time-scale domain to match wide-band signals that are better modeled in terms of time shifts and scale changes than in terms of time and frequency shifts. Using a wavelet decomposition and the Bertrand time-scale distribution, we locally balance linearity and bilinearity in order to provide good resolution while suppressing troublesome interference components. The theory of frames provides a unifying perspective for cross-term deleted representations in general