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Weiss–Weinstein Bound on Multiple Change-Points Estimation

Bacharach, Lucien and Renaux, Alexandre and Korso, Mohammed Nabil El and Chaumette, Éric Weiss–Weinstein Bound on Multiple Change-Points Estimation. (2017) IEEE Transactions on Signal Processing, 65 (10). 2686-2700. ISSN 1053-587X

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Official URL: https://doi.org/10.1109/TSP.2017.2673804

Abstract

In the context of multiple change-points estimation, performance analysis of estimators such as the maximum likelihood is often difficult to assess since the regularity assumptions are not met. Focusing on the estimators variance, one can, however, use lower bounds on themean square error. In this paper,we derive the so-called Weiss–Weinstein bound (WWB) that is known to be an efficient tool in signal processing to obtain a fair overview of the estimation behavior. Contrary to several works about performance analysis in the change-point literature, our study is adapted to multiple changes. First, useful formulas are given for a general estimation problem whatever the considered distribution of the data. Second, closed-form expressions are given in the cases of Gaussian observations with changes in the mean and/or the variance, and changes in the mean rate of a Poisson distribution. Furthermore, a semidefinite programming formulation of the minimization procedure is given in order to compute the tightest WWB. Specifically, it consists of finding the unique minimum volume covering the set constituted by hyperellipsoid elements that are generated using the derived candidateWWBmatrices w.r.t. the so-called Loewner partial ordering. Finally, simulation results are provided to show the good behavior of the proposed bound.

Item Type:Article
Additional Information:Thanks to the IEEE (Institute of Electrical and Electronics Engineers). This paper is available at : https://ieeexplore.ieee.org/document/7862907 “© 2017 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.
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
Other partners > CentraleSupélec (FRANCE)
Other partners > Université Paris Ouest Nanterre La Défense (FRANCE)
Other partners > Université Paris-Sud 11 (FRANCE)
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Deposited By: Eric Chaumette
Deposited On:30 Apr 2019 07:04

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