Adaptive estimates of linear functionals |
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| Authors: | Sam Efromovich Mark G. Low |
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| Affiliation: | (1) Department of Mathematics and Statistics, University of New Mexico, 17131 Albuquerque, NM, USA;(2) Department of Statistics, Wharton School, University of Pennsylvania, 19104 Philadelphia, PA, USA |
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| Abstract: | Summary Given a collection of nested closed, convex symmetric sets and a linear functional, we find estimates which are within a logarithm term of being simultaneously asymptotically minimax. Moreover, these estimates can be constructed so that the loss of this logarithm term only occurs on a small subset of functions. These estimates are quasi-optimal since there do not exist estimators which do not lose a logarithm term on some part of the parameter spaces.This author was partially supported by an NSF Grant DMS-9123956This author was supported by an NSF Postdoctoral Research Fellowship |
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| Keywords: | 62C05 62E20 62J02 62G05 62M99 |
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