New Approach to Optimization of Stable Estimation

Shurygin, A. M.

doi:10.1007/978-94-011-0854-6_15

Cited by 6 publications

(14 citation statements)

References 9 publications

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“…In (Shurygin, 1994a(Shurygin, , 1994b(Shurygin, , 2000a(Shurygin, , 2000b a new measure of an estimator's sensitivity, derived from the asymptotic variance V (ψ, f ) is introduced. Formally, he derived it as…”

Section: Variance Sensitivitymentioning

confidence: 99%

“…Under this point of view, exploring the range of the variance sensitivity and of the efficiency at a given density is all that remains to be done. As shown in (Shurygin, 1994a(Shurygin, , 1994b(Shurygin, , 2000a(Shurygin, , 2000b, the solution of the problem is given by…”

Section: Stability Of An Estimatormentioning

confidence: 99%

“…Setting different weights for efficiency and stability, various optimality criteria can be constructed (Shurygin, 1994a(Shurygin, , 1994b(Shurygin, , 2000a(Shurygin, , 2000b. In particular, the structure of redescenders is specified by the analog of Hampel's lemma (Hampel et.…”

Section: Stability Of An Estimatormentioning

confidence: 99%

“…Among these, we recommend the radical M -estimator, which is at the same time highly efficient and stable (see Table 1; Shurygin, 1994aShurygin, , 1994bShurygin, , 2000aShurygin, , 2000bShevlyakov et.al., 2005).…”

Section: Optimal Redescending M -Estimatorsmentioning

confidence: 99%

“…Finally, it is noteworthy that the Shurygin's global stability approach used in this paper can be extended to the problems of robust estimation of scale, regression, multivariate location and scatter (Shurygin, 1994a(Shurygin, , 1994b(Shurygin, , 1995(Shurygin, , 1996(Shurygin, , 2000a(Shurygin, , 2000b.…”

Section: Optimal Redescending M -Estimatorsmentioning

confidence: 99%

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Redescending M-estimators

Shevlyakov

Morgenthaler

Shurygin

2008

Journal of Statistical Planning and Inference

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In finite sample studies redescending M -estimators outperform bounded M -estimators (see for example, Andrews et al., 1972). Even though redescenders arise naturally out of the maximum likelihood approach if one uses very heavy-tailed models, the commonly used redescenders have been derived from purely heuristic considerations. Using a recent approach proposed by Shurygin, we studied the optimality of redescending M -estimators. We show that redescending M -estimator can be designed by applying a global minimax criterion to locally robust estimators, namely maximizing the minimum variance sensitivity of an estimator over a given class of densities. As a particular result, we proved that Smith's estimator, which is a compromise between Huber's skipped mean and Tukey's biweight, provides the guaranteed level of an estimator's variance sensitivity over the class of distribution densities with a bounded variance.

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Section: Variance Sensitivitymentioning

confidence: 99%

Section: Stability Of An Estimatormentioning

confidence: 99%

Section: Stability Of An Estimatormentioning

confidence: 99%

Section: Optimal Redescending M -Estimatorsmentioning

confidence: 99%

Section: Optimal Redescending M -Estimatorsmentioning

confidence: 99%

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Redescending M-estimators

Shevlyakov

Morgenthaler

Shurygin

2008

Journal of Statistical Planning and Inference

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Asymptotically stable detection of a weak signal

Shevlyakov

Shin

Lee

et al. 2013

Adaptive Control & Signal

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To design highly efficient and robust detectors of a weak signal, an asymptotic approach to stable estimation exploiting redescending score functions is used. Two new indicators of robustness of detection, the detection error sensitivity and detection stability, are introduced. The optimal Neyman-Pearson rules maximizing detection efficiency under the guaranteed level of detection stability are written out. Under heavy-tailed noise distributions, the proposed asymptotically stable detectors based on redescending score functions, namely, the minimum error sensitivity and the radical ones, outperform conventional linear bounded Huber's and redescending Hampel's detectors both on small and large samples.

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Asymptotically Stable Tests with Application to Robust Detection

Shevlyakov

2016

Recent Advances in Robust Statistics: Theory and Applications

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New Approach to Optimization of Stable Estimation

Cited by 6 publications

References 9 publications

Redescending M-estimators

Redescending M-estimators

Asymptotically stable detection of a weak signal

Asymptotically Stable Tests with Application to Robust Detection

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