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- W2036767512 abstract "An unknown signal plus white noise is observed at $n$ discrete time points. Within a large convex class of linear estimators of $xi$, we choose the estimator $hat{xi}$ that minimizes estimated quadratic risk. By construction, $hat{xi}$ 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 $hat{xi}$ is asymptotically minimax in Pinsker’s sense over certain ellipsoids in the parameter space and shares one such asymptotic minimax property with the James–Stein estimator. We describe computational algorithms for $hat{xi}$ and construct confidence sets for the unknown signal. These confidence sets are centered at $hat{xi}$, have correct asymptotic coverage probability and have relatively small risk as set-valued estimators of $xi$." @default.
- W2036767512 created "2016-06-24" @default.
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- W2036767512 date "1998-10-01" @default.
- W2036767512 modified "2023-10-14" @default.
- W2036767512 title "Modulation of estimators and confidence sets" @default.
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- W2036767512 doi "https://doi.org/10.1214/aos/1024691359" @default.
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