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   -> Volume 11, Issue 1


Preprint: A wavelet-Fisz algorithm for Poisson intensity estimation
 
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Piotr Fryzlewicz (P.Z.Fryzlewicz@bristol.ac.uk)
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PostPosted: Tue Jul 02, 2002 5:54 pm    
Subject: Preprint: A wavelet-Fisz algorithm for Poisson intensity estimation
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Title: A wavelet-Fisz algorithm for Poisson intensity estimation

Authors: Piotr Fryzlewicz and Guy P. Nason, University of Bristol, UK

Abstract:
This article introduces a new method for the estimation of the intensity of an inhomogeneous one-dimensional Poisson process. The wavelet-Fisz transformation transforms a vector of binned Poisson counts to approximate normality with variance one. Theory shows that, asymptotically, the transformed vector is normal and the elements uncorrelated. Hence we can use any suitable Gaussian wavelet shrinkage method to estimate the Poisson intensity. Since the wavelet-Fisz operator does not commute with the shift operator we can dramatically improve accuracy by always cycle spinning before the wavelet-Fisz transform as well as optionally after.

Extensive simulations show that our approach was never worse than any of the state-of-the-art competitorsand usually significantly outperformed them. Our method is fast, simple, automatic and easy to code. The wavelet-Fisz principle extends to many dimensions and would also be able to handle several types of noise including binomial, negative binomial and Gamma.

Our technique is applied to the estimation of the intensity of earthquakes in northern California. We show that our technique gives visually similar results to the current state-of-the-art.

URL: http://www.stats.bris.ac.uk/pub/ResRept/2002/08.ps.gz

Piotr Fryzlewicz
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