Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data: Rejoinder

Good, I. J.; Gaskins, R. A.

doi:10.2307/2287385

Cited by 2 publications

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“…An alternative technique to improve traditional estimates which is prevalent in the literature is the use of regularization, first systematically studied by Tikhonov [135,136] and later extended to general estimation problems via the penalized ML (PML) approach [65,66]. In general, regularization methods measure both the fit to the observed data and the physical plausibility of the estimate.…”

Section: Introductionmentioning

confidence: 99%

Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound

Eldar

2007

FNT in Signal Processing

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One of the prime goals of statistical estimation theory is the development of performance bounds when estimating parameters of interest in a given model, as well as constructing estimators that achieve these limits. When the parameters to be estimated are deterministic, a popular approach is to bound the mean-squared error (MSE) achievable within the class of unbiased estimators. Although it is well-known that lower MSE can be obtained by allowing for a bias, in applications it is typically unclear how to choose an appropriate bias.In this survey we introduce MSE bounds that are lower than the unbiased Cramér-Rao bound (CRB) for all values of the unknowns. We then present a general framework for constructing biased estimators with smaller MSE than the standard maximum-likelihood (ML) approach, regardless of the true unknown values. Specializing the results to the linear Gaussian model, we derive a class of estimators that dominate least-squares in terms of MSE. We also introduce methods for choosing regularization parameters in penalized ML estimators that outperform standard techniques such as cross validation.

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Section: Introductionmentioning

confidence: 99%

Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound

Eldar

2007

FNT in Signal Processing

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show abstract

“…The strategy we outlined is based on first developing MSE performance bounds, and then designing estimators that achieve these limits, thus ensuring MSE improvement over existing unbiased solutions. An alternative technique to improve traditional estimates which is prevalent in the literature is the use of regularization, first systematically studied by Tikhonov [135,136] and later extended to general estimation problems via the penalized ML (PML) approach [65,66]. In general, regularization methods measure both the fit to the observed data and the physical plausibility of the estimate.…”

Section: Introductionmentioning

confidence: 99%

Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound

Eldar

2007

View full text Add to dashboard Cite

show abstract

Density Estimation and Bump-Hunting by the Penalized Likelihood Method Exemplified by Scattering and Meteorite Data: Rejoinder

Cited by 2 publications

References 0 publications

Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound

Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound

Rethinking Biased Estimation: Improving Maximum Likelihood and the Cramér–Rao Bound

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