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Conference proceeding
Wavelet-Based Detection and Estimation of Fractional Lévy Signals in High Dimensions
Proceedings of CAMSAP 2019, pp 574-578
15 Dec 2019
Abstract
In the modern world, systems are routinely monitored by multiple sensors, generating "Big Data" in the form of a large collection of time series. However, dynamic signals are often low-dimensional and characterized by joint scale-free dynamics (self-similarity) and non-Gaussianity. In this paper, we put forward a statistical methodology for identifying the number of multivariate self-similar, Lévydriven components immersed in high-dimensional noise, as well as for estimating the underlying scaling exponents. It relies on the analysis of the evolution over scales of the eigenvalues of random wavelet matrices. Monte Carlo simulations show that the proposed methodology is accurate for realistic sample sizes. This holds even at low signal-to-noise ratios and for a large number of observed mixed and noisy time series. The mathematical framework further allows us to analyze the impact of the tails of the Lévy noise marginal distribution on the estimation performance.
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2 citations in Scopus
Details
- Title
- Wavelet-Based Detection and Estimation of Fractional Lévy Signals in High Dimensions
- Creators
- B Boniece - Washington University in Saint LouisHerwig Wendt - Université de ToulouseGustavo Didier - Tulane UniversityPatrice Abry - École Normale Supérieure de Lyon
- Publication Details
- Proceedings of CAMSAP 2019, pp 574-578
- Conference
- IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP 2019), 8th (2019)
- Series
- 2019 IEEE 8th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP)
- Publisher
- The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
- Resource Type
- Conference proceeding
- Language
- English
- Academic Unit
- Mathematics
- Scopus ID
- 2-s2.0-85082385804
- Other Identifier
- 991021861862404721