JSM 2005 Online Program

Abstract #303230

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Activity Number:	395
Type:	Contributed
Date/Time:	Wednesday, August 10, 2005 : 10:30 AM to 12:20 PM
Sponsor:	Section on Nonparametric Statistics
Abstract - #303230
Title:	Change Point Detection by Unbalance Continuous Wavelet Analysis
Author(s):	Maarten Jansen*+
Companies:	Technische Universiteit Eindhoven
Address:	PO Box 513, Eindhoven, 5600MB, Netherlands
Keywords:	wavelet ; Poisson ; change point ; lifting
Abstract:	We present a continuous wavelet analysis of count data with time-varying intensities. The objective is to jump in the intensity curve. We allow multiple change points in the intensity curve without specifying the number of change points in advance. We extend the classical (discretised) continuous Haar wavelet analysis toward an unbalanced (i.e., asymmetric) version. This additional degree of freedom allows more powerful detection. This analysis can be seen as an instance of so-called second generation wavelets. Locations of intensity change points are identified as persistent local maxima in the wavelet analysis at the successive scales. Unlike existing methods (Mallat, Hwang, Zhong), the presented algorithm does not locate the precise change point position by looking at fine-scale behavior. It rather finds the optimal scale for the analysis. Although the method is presented here in the context of Poisson (count) data, the ideas also work for the detection of multiple change points in other circumstances (such as additive Gaussian noise).

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