Mathematics, Systems and Robotics Seminar  RSS

Sessions
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09/01/2004, 15:00 — 16:00 — Conference Room, Instituto de Sistemas e Robótica, North Tower, 7th floor, IST
Paulo Gonçalves and Jorge Silva, ISR/IST and CAM/IST

"Diverging Moments and Parameter Estimation" and "Wavelets and Applications"

  • Paulo Gonçalves - Diverging moments and parameter estimation

    Abstract: When dealing with finite size data sets of an unknown heavy tailed distributions, standard empirical estimators of moments will typically fail to reflect the theoretical divergence of moments and provide finite estimates for all order moments. We propose a wavelet-based estimator for the characteristic exponents ( C -,C +) of a random variable, which bound the interval of all orders C - <r<C + with finite moment. This objective is achieved by deriving a theoretical equivalence between finiteness of moments and the local Holder regularity of the characteristic function at the origin, and by deriving a wavelet based estimation scheme which is particularly suited to characteristic functions.

  • Jorge Silva - Wavelets and Applications

    Abstract: In this presentation we give a short overview of the theory of wavelets trying to compare it with the classical theory of Fourier series. We discuss the advantages of this approach pointing out some applications.

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