Wavelet-Based Estimation for Univariate Stable Laws |
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Authors: | Anestis Antoniadis Andrey Feuerverger Paulo Gonçalves |
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Institution: | 1. Laboratoire IMAG-LMC, University Joseph Fourier, BP 53, 38041, Grenoble Cedex 9, France 2. Department of Statistics, University of Toronto, Toronto, ON, Canada, M5S 3G3 3. INRIA Rh?ne-Alpes, ZIRST, 655 Avenue de l’Europe, 38330, Monbonnot Saint Martin, France
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Abstract: | Stable distributions are characterized by four parameters which can be estimated via a number of methods, and although approximate
maximum likelihood estimation techniques have been proposed, they are computationally intensive and difficult to implement.
This article describes a fast, wavelet-based, regression-type method for estimating the parameters of a stable distribution.
Fourier domain representations, combined with a wavelet multiresolution approach, are shown to be effective and highly efficient
tools for inference in stable law families. Our procedures are illustrated and compared with other estimation methods using
simulated data, and an application to a real data example is explored. One novel aspect of this work is that here wavelets
are being used to solve a parametric problem, rather than a nonparametric one, which is the more typical context in wavelet
applications. |
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Keywords: | Wavelets Stable laws Empirical characteristic function Estimation Efficiency Completeness Regularization |
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