Wavelet based estimator for the self-similarity parameter of α-stable processes

Author

Abry, Patrice ; Delbeke, Lieve ; Flandrin, Patrick

Author_Institution

ENS, CNRS, Lyon, France

Volume

3

fYear

1999

fDate

15-19 Mar 1999

Firstpage

1729

Abstract

We, study self-similar processes with possibly infinite second order statistics and long-range dependence. To do so, we detail the statistical properties of the wavelet coefficients of α-stable self similar processes, used as a paradigm for those situations. We, then, propose a wavelet based estimator for the self-similarity parameter and analyse its statistical performance both theoretically and numerically. We show that it is unbiased, that its variance decreases as the inverse of the length of the data and that it can be easily implemented

Keywords

fractals; parameter estimation; stability; statistical analysis; wavelet transforms; α-stable self similar processes; infinite second order statistics; inverse data length; long-range dependence; self-similarity parameter; statistical performance; statistical properties; symmetric α-stable processes; unbiased estimator; variance; wavelet based estimator; wavelet coefficients; Brownian motion; Data analysis; ISO; Mathematics; Performance analysis; Statistical analysis; Statistics; Wavelet analysis; Wavelet coefficients; Wavelet transforms;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1999. Proceedings., 1999 IEEE International Conference on

Conference_Location

Phoenix, AZ

ISSN

1520-6149

Print_ISBN

0-7803-5041-3

Type

conf

DOI

10.1109/ICASSP.1999.756328

Filename

756328