The Risk-Unbiased Cramér–Rao Bound for Non-Bayesian Multivariate Parameter Estimation

Bar, Shahar; Tabrikian, Joseph

doi:10.1109/tsp.2018.2863663

Cited by 4 publications

(4 citation statements)

References 62 publications

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“…That is, the selection of the parameter of interest is independent of the data. In particular, for p m = 1 m=m0 , where θ m0 is the parameter of interest, we obtain the well-known problem of non-Bayesian estimation in the presence of additional deterministic nuisance parameters [2], [3], [49].…”

Section: B Special Casesmentioning

confidence: 99%

“…the considered cost function (see e.g. [3], [38], [50], [51]). The Lehmann unbiasedness for two-stage estimation after parameter selection w.r.t.…”

Section: Two-stage Psmse and ψ-Unbiasednessmentioning

confidence: 99%

“…Parameter estimation in the presence of nuisance parameters is of great interest in many signal-processing applications [1]- [3]. Estimation after parameter selection refers to the problem in which the choice of the parameter of interest (and, as a result, the nuisance parameters) is made by a data-based selection rule.…”

Section: Introductionmentioning

confidence: 99%

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Low-Complexity Methods for Estimation After Parameter Selection

Harel

Routtenberg

2020

IEEE Trans. Signal Process.

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Statistical inference of multiple parameters often involves a preliminary parameter selection stage. The selection stage has an impact on subsequent estimation, for example by introducing a selection bias. The post-selection maximum likelihood (PSML) estimator is shown to reduce the selection bias and the post-selection mean-squared-error (PSMSE) compared with conventional estimators, such as the maximum likelihood (ML) estimator. However, the computational complexity of the PSML is usually high due to the multi-dimensional exhaustive search for a global maximum of the post-selection log-likelihood (PSLL) function. Moreover, the PSLL involves the probability of selection that, in general, does not have an analytical form. In this paper, we develop new low-complexity post-selection estimation methods for a two-stage estimation after parameter selection architecture. The methods are based on implementing the iterative maximization by parts (MBP) approach, which is based on the decomposition of the PSLL function into "easilyoptimized" and complicated parts.The proposed second-best PSML method applies the MBP-PSML algorithm with a pairwise probability of selection between the two highest-ranked parameters w.r.t. the selection rule. The proposed SA-PSML method is based on using stochastic approximation (SA) and Monte Carlo integrations to obtain a non-parametric estimation of the gradient of the probability of selection and then applying the MBP-PSML algorithm on this approximation. For low-complexity performance analysis, we develop the empirical post-selection Cramér-Rao-type lower bound. Simulations demonstrate that the proposed post-selection estimation methods are tractable and reduce both the bias and the PSMSE, compared with the ML estimator, while only requiring moderate computational complexity.

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Section: B Special Casesmentioning

confidence: 99%

“…the considered cost function (see e.g. [3], [38], [50], [51]). The Lehmann unbiasedness for two-stage estimation after parameter selection w.r.t.…”

Section: Two-stage Psmse and ψ-Unbiasednessmentioning

confidence: 99%

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Low-Complexity Methods for Estimation After Parameter Selection

Harel

Routtenberg

2020

IEEE Trans. Signal Process.

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“…In order to set a benchmark before designing an estimator, we now evaluate the Hybrid Cramér-Rao Bound (HCRB) [36][37][38][39] for the hybrid parameter estimation problem proposed in Section 3. The HCRB provides a lower bound on the error covariance matrix of the estimator of a hybrid unknown parameter vector.…”

Section: Hybrid Cramér-rao Boundmentioning

confidence: 99%

Design and Analysis of a Non-Iterative Estimator for Target Location in Multistatic Sonar Systems with Sensor Position Uncertainties

Wang

Yang

et al. 2020

Mathematics

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Target location is the basic application of a multistatic sonar system. Determining the position/velocity vector of a target from the related sonar observations is a nonlinear estimation problem. The presence of possible sensor position uncertainties turns this problem into a more challenging hybrid parameter estimation problem. Conventional gradient-based iterative estimators suffer from the problems of initialization difficulties and local convergence. Even if there is no problem with initialization and convergence, a large computational cost is required in most cases. In view of these drawbacks, we develop a computationally efficient non-iterative position/velocity estimator. The main numerical computation involved is the weighted least squares optimization, which makes the estimator computationally efficient. Parameter transformation, model linearization and two-stage processing are exploited to prevent the estimator from iterative computation. Through performance analysis and experimental verification, we find that the proposed estimator reaches the hybrid Cramér–Rao bound and has linear computational complexity.

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