Abstract.
We consider adaptive estimating the value of a linear functional from indirect white noise observations. For a flexible approach, the problem is embedded in an abstract Hilbert scale. We develop an adaptive estimator that is rate optimal within a logarithmic factor simultaneously over a wide collection of balls in the Hilbert scale. It is shown that the proposed estimator has the best possible adaptive properties for a wide range of linear functionals. The case of discretized indirect white noise observations is studied, and the adaptive estimator in this setting is developed.
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Received: 5 May 1999 / Revised version: 25 October 1999 / Published online: 5 September 2000
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Goldenshluger, A., Pereverzev, S. Adaptive estimation of linear functionals in Hilbert scales from indirect white noise observations. Probab Theory Relat Fields 118, 169–186 (2000). https://doi.org/10.1007/s440-000-8013-3
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DOI: https://doi.org/10.1007/s440-000-8013-3