A wavelet based likelihood ratio test for the homogeneity of poisson processes

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Title: A wavelet based likelihood ratio test for the homogeneity of poisson processes
Author(s): Taleb, Y
Cohen, E
Item Type: Conference Paper
Abstract: Estimating the rate (first-order intensity) of a point process is a task of great interest in the understanding of its nature. In this work we first address the estimation of the rate of an orderly point process on the real line using a multiresolution wavelet expansion approach. Implementing Haar wavelets, we find that in the case of a Poisson process the piecewise constant wavelet estimator of the rate has a scaled Poisson distribution. We apply this result in the design of a likelihood ratio test for a multiresolution formulation of the homogeneity of a Poisson process. We demonstrate this method with simulations and provide Type 1 error and empirical power plots under specific models.
Publication Date: 25-Aug-2016
Date of Acceptance: 27-Apr-2016
URI: http://hdl.handle.net/10044/1/32818
DOI: http://dx.doi.org/10.1109/SSP.2016.7551768
ISBN: 978-1-4673-7803-1
Publisher: IEEE
Journal / Book Title: Proceedings of the 2016 IEEE Statistical Signal Processing Workshop (SSP)
Copyright Statement: © 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Conference Name: 2016 IEEE Statistical Signal Processing Workshop (SSP)
Publication Status: Published
Start Date: 2016-06-26
Finish Date: 2016-06-29
Conference Place: Majorca, Spain
Appears in Collections:Mathematics
Statistics
Faculty of Natural Sciences



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