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Modulation Estimators and Confidence Sets

Beran, Rudolf ; Dümbgen, Lutz

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Abstract

An unknown signal plus white noise is observed at n discretetime points. Within a large convex class of linear estimators of the signal, we choose the one which minimizes estimated quadratic risk. By construction,the resulting estimator is nonlinear. This estimation is done after orthogonal transformation of the data to a reasonable coordinate system. The procedure adaptively tapers the coefficients of the transformed data. If the class of candidate estimators satisfies a uniform entropy condition, then our estimator is asymptotically minimax in Pinsker's sense over certain ellipsoids in the parameter space and dominates the James-Stein estimatorasymptotically. We describe computational algorithms for the modulation estimator and construct confidence sets for the unknown signal.These confidence sets are centered at the estimator, have correctasymptotic coverage probability, and have relatively small risk asset-valued estimators of the signal.

Item Type: Working paper
Place of Publication: Heidelberg
Edition: January 1996, revised August 1997
Date Deposited: 09 Jun 2016 07:58
Date: August 1997
Number of Pages: 36
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 310 General statistics
510 Mathematics
Uncontrolled Keywords: Adaptivity, asymptotic minimax, bootstrap, bounded Variation; coverage probability; isotonic regression; orthogonal transformation; signal recovery; Stein's unbiased estimator of risk; tapering
Schriftenreihe ID: Beiträge zur Statistik > Beiträge
Additional Information: Auch erschienen in: Annals of Statistics 26 (1998), pp. 1826-1856
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