Diverging moments and parameter estimation

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Title: Diverging moments and parameter estimation
Author: Goncalves, Paulo; Riedi, Rudolf H.
Type: Journal article
Keywords: Diverging moments; heavy tail distributions; characteristic functions; wavelet transform; multifractal analysis.
Citation: P. Goncalves and R. H. Riedi, "Diverging moments and parameter estimation," Journal of the American Statistical Association, 2004.
Abstract: Heavy 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.
Date Published: 2004-01-15

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