Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4605036 | Applied and Computational Harmonic Analysis | 2015 | 6 Pages |
Abstract
Using wavelet analysis we show that if the characteristic function of a random variable X can be approximated at 0 by some polynomial of even degree 2p then the moment of order 2p of X exists. This strengthens a Tauberian-type result by Ramachandran and implies that the characteristic function is actually 2p times differentiable at 0. This fact also provides the theoretical basis for a wavelet based non-parametric estimator of the tail index of a distribution.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
R. Riedi, P. Gonçalves,