Weiss-Weinstein bound for change-point estimation

IEEE Trans. Signal Process.

Korso

et al. 2017

Self Cite

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 the mean 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 candidate WWB matrices w.r.t. the so-called Loewner partial ordering. Finally, simulation results are provided to show the good behavior of the proposed bound.

Section: Introductionmentioning

confidence: 99%

Weiss–Weinstein Bound on Multiple Change-Points Estimation

Bacharach

IEEE Trans. Signal Process.

Korso

et al. 2017

Self Cite

“…To conclude, equations (17), (19), (20), (24), (25), (32), (33) and (34) provide all the expressions necessary to determine the elements of the matrix W (H, s) CV −1 C T in (16). It is worth noticing that, due to the structure of the matrices V 11 , V 12 and V 22 , the inversion of V should not be particularly difficult from a computational point of view.…”

Section: ) Block V 11mentioning

confidence: 99%

“…We finally obtain the HB for a Poisson distributed signal that includes Q change-points by plugging these last expressions into the equations (17), (19), (20), (24), (25), (32), (33) and (34) from Section IV-A, and by applying the procedure described in Section III-C, which leads to the tightest bound.…”

Section: B Gaussian and Poisson Distributionsmentioning

confidence: 99%

“…This work was later extended by La Rosa et al to the case of multiple changepoints [16]. Since these deterministic bounds only give a coarse insight on the change-point estimation behavior, we recently proposed the use of Bayesian lower bounds such as the Weiss-Weinstein bound (WWB), both for a single change [17] and multiple changes [18]. It is worth mentioning that to the best of our knowledge, most of the derived bounds in the literature considered the change-points as the only unknown parameters, meaning that all the other parameters were assumed to be known (e.g., in [18], the means and variances of the Gaussian distributions associated with the different segments were assumed to be known).…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Hybrid Lower Bound for Parameter Estimation of Signals With Multiple Change-Points

Bacharach

Korso

IEEE Trans. Signal Process.

et al. 2019

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Change-point estimation has received much attention in the literature as it plays a significant role in several signal processing applications. However, the study of the optimal estimation performance in such context is a difficult task since the unknown parameter vector of interest may contain both continuous and discrete parameters, namely the parameters associated with the noise distribution and the change-point locations. In this paper, we handle this by deriving a lower bound on the mean square error of these continuous and discrete parameters. Specifically, we propose a hybrid Cramér-Rao-Weiss-Weinstein bound and derive its associated closed-form expressions. Numerical simulationsassess the tightness of the proposed bound in the case of Gaussian and Poisson observations.

“…The Chapman-Robbins bound has been derived in [14] in the context of one change point and extended to the multiple change point problem in [15]. In the Bayesian context, the Weiss-Weinstein bound has been studied in [16]- [18]. In this paper, we stay in the non-Bayesian context to study the Barankin (or McAulay-Seidman bound) [19], [20] for a change point estimation problem when (contrary to previous works) two sets of non synchronized data are available.…”

Section: Introductionmentioning

confidence: 99%

Performance Bounds for Change Point and Time Delay Estimation

Ren

2018 26th European Signal Processing Conference (EUSIPCO)

Azarian

2018

Self Cite

This paper investigates performance bounds for joint estimation of signal change point and time delay estimation between two receivers. This problem is formulated as an estimation of the beginning of a well known message and the time shift of its arrival on two receivers from a noisy source. This scenario could be viewed as an extension of the classical time delay estimation [1], [2] with an additional change on the transmitted message. A theoretical derivation of the Barankin bound and a simplified version of this bound are proposed in order to predict the Maximum Likelihood Estimator (MLE) behavior. Simulations illustrate the validity of both bounds but it is pointed out that the MLE seems asymptotically efficient for the normalized time shift estimation contrary to the estimation of message's starting time.