Barankin Bounds on Parameter Estimation

McAulay, R.; Hofstetter, E.

doi:10.1109/tit.1971.1054719

Cited by 123 publications

(62 citation statements)

References 9 publications

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“…we consider an interval around each of the 48 local maxima). Let (83) be the MSEA based on (22) and using the interval probability approximation ( , see (26), (27), (29)) and interval mean and variance approximations and (…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…However, it can be computed numerically using for example the MATLAB function QSCMVNV (written by Genz based on [50]- [53]) that computes the multivariate normal probability with integration region specified by a set of linear inequalities in the form . Using QSCMVNV, can be approximated by: (26) where is the number of points used by the algorithm (e.g., ), and two -column vectors, and an matrix with and 6 . 6 We denote by the identity matrix of rank , and and the zero and one matrices of dimension .…”

Section: A Computation Of the Interval Probabilitymentioning

confidence: 99%

“…In this subsection we have seen that the interval probability in (23) can be approximated by in (26) or in (29), and upper bounded by in (27). The UB is adopted in [1], [15], [41], [43], [44] with minor modifications; in fact, is approximated by one in [1] and by in [15], [41], [43], [44].…”

Section: ) Analytic Approximationmentioning

confidence: 99%

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Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

Mallat

Gezici

Dardari

et al. 2014

IEEE Trans. Signal Process.

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Abstract-In nonlinear deterministic parameter estimation, the maximum likelihood estimator (MLE) is unable to attain the Cramér-Rao lower bound at low and medium signal-to-noise ratios (SNRs) due the threshold and ambiguity phenomena. In order to evaluate the achieved mean-squared error (MSE) at those SNR levels, we propose new MSE approximations (MSEA) and an approximate upper bound by using the method of interval estimation (MIE). The mean and the distribution of the MLE are approximated as well. The MIE consists in splitting the a priori domain of the unknown parameter into intervals and computing the statistics of the estimator in each interval. Also, we derive an approximate lower bound (ALB) based on the Taylor series expansion of noise and an ALB family by employing the binary detection principle. The accuracy of the proposed MSEAs and the tightness of the derived approximate bounds are validated by considering the example of time-of-arrival estimation.Index Terms-Nonlinear estimation, threshold and ambiguity phenomena, maximum likelihood estimator, mean-squared error, upper and lowers bounds, time-of-arrival.

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Section: Numerical Results and Discussionmentioning

confidence: 99%

Section: A Computation Of the Interval Probabilitymentioning

confidence: 99%

See 1 more Smart Citation

Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

Mallat

Gezici

Dardari

et al. 2014

IEEE Trans. Signal Process.

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show abstract

“…Nevertheless, the BB plays a central role, from the theoretical point of view, as it provides a hierarchy of weaker bounds which can be used in practice with estimators that are asymptotically unbiased. The BB can be written as [44] …”

Section: Barankin Boundmentioning

confidence: 99%

Frequentist and Bayesian Quantum Phase Estimation

Pezzé

Gessner

et al. 2018

Entropy

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Frequentist and Bayesian phase estimation strategies lead to conceptually different results on the state of knowledge about the true value of an unknown parameter. We compare the two frameworks and their sensitivity bounds to the estimation of an interferometric phase shift limited by quantum noise, considering both the cases of a fixed and a fluctuating parameter. We point out that frequentist precision bounds, such as the Cramér-Rao bound, for instance, do not apply to Bayesian strategies and vice versa. In particular, we show that the Bayesian variance can overcome the frequentist Cramér-Rao bound, which appears to be a paradoxical result if the conceptual difference between the two approaches are overlooked. Similarly, bounds for fluctuating parameters make no statement about the estimation of a fixed parameter.

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“…Barankin bound [13], [14], [15], [16]) for breakdown estimation may be an alternative approach, but a specific estimator in general does not achieve the bound. The breakdown point provided is therefore usually over-optimistic.…”

Section: Introductionmentioning

confidence: 99%

Guaranteed Performance in the FRI Setting

Wei

Dragotti

2015

IEEE Signal Process. Lett.

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Abstract-Finite Rate of Innovation (FRI) sampling theory has shown that it is possible to sample and perfectly reconstruct classes of non-bandlimited signals such as streams of Diracs. In the case of noisy measurements, FRI methods achieve the optimal performance given by the Cramér-Rao bound up to a certain PSNR and breaks down for smaller PSNRs.To the best of our knowledge, the precise anticipation of the breakdown event in FRI settings is still an open problem. In this paper, we address this issue by investigating the subspace swap event which has been broadly recognised as the reason for performance breakdown in SVD-based parameter estimation algorithms. We work out at which noise level the absence of subspace swap is guaranteed and this gives us an accurate prediction of the breakdown PSNR which we also relate to the sampling rate and the distance between adjacent Diracs. Simulation results validate the reliability of our analysis.

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Barankin Bounds on Parameter Estimation

Cited by 123 publications

References 9 publications

Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

Frequentist and Bayesian Quantum Phase Estimation

Guaranteed Performance in the FRI Setting

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Barankin Bounds on Parameter Estimation

Cited by 123 publications

References 9 publications

Statistics of the MLE and Approximate Upper and Lower Bounds&#x2014;Part I: Application to TOA Estimation

Statistics of the MLE and Approximate Upper and Lower Bounds&#x2014;Part I: Application to TOA Estimation

Frequentist and Bayesian Quantum Phase Estimation

Guaranteed Performance in the FRI Setting

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Product

Resources

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Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation

Statistics of the MLE and Approximate Upper and Lower Bounds—Part I: Application to TOA Estimation