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Adaptive estimates of linear functionals
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  • Published: June 1994

Adaptive estimates of linear functionals

  • Sam Efromovich1 &
  • Mark G. Low2 

Probability Theory and Related Fields volume 98, pages 261–275 (1994)Cite this article

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.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of New Mexico, 17131, Albuquerque, NM, USA

    Sam Efromovich

  2. Department of Statistics, Wharton School, University of Pennsylvania, 19104, Philadelphia, PA, USA

    Mark G. Low

Authors
  1. Sam Efromovich
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  2. Mark G. Low
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Additional information

This author was partially supported by an NSF Grant DMS-9123956

This author was supported by an NSF Postdoctoral Research Fellowship

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Cite this article

Efromovich, S., Low, M.G. Adaptive estimates of linear functionals. Probab. Th. Rel. Fields 98, 261–275 (1994). https://doi.org/10.1007/BF01192517

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  • Received: 04 August 1992

  • Revised: 06 July 1993

  • Issue Date: June 1994

  • DOI: https://doi.org/10.1007/BF01192517

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Mathematics Subject Classification (1991)

  • 62C05
  • 62E20
  • 62J02
  • 62G05
  • 62M99
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