Adaptation under probabilistic error for estimating linear functionals |
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Authors: | T Tony Cai Mark G Low |
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Institution: | Department of Statistics, The Wharton School, University of Pennsylvania, Philadelphia, PA 19104, USA |
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Abstract: | The problem of estimating linear functionals based on Gaussian observations is considered. Probabilistic error is used as a measure of accuracy and attention is focused on the construction of adaptive estimators which are simultaneously near optimal under probabilistic error over a collection of convex parameter spaces. In contrast to mean squared error it is shown that fully rate optimal adaptive estimators can be constructed for probabilistic error. A general construction of such estimators is provided and examples are given to illustrate the general theory. |
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Keywords: | primary 62G99 secondary 62F12 62F35 62M99 |
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