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Adaptation under probabilistic error for estimating linear functionals

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  • Tony Cai, T.
  • Low, Mark G.

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.

Suggested Citation

  • Tony Cai, T. & Low, Mark G., 2006. "Adaptation under probabilistic error for estimating linear functionals," Journal of Multivariate Analysis, Elsevier, vol. 97(1), pages 231-245, January.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:1:p:231-245
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    References listed on IDEAS

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    1. Low, Mark G. & Kang, Yung-Gyung, 2002. "Estimating monotone functions," Statistics & Probability Letters, Elsevier, vol. 56(4), pages 361-367, February.
    2. Efromovich, Sam, 1994. "On adaptive estimation of nonlinear functionals," Statistics & Probability Letters, Elsevier, vol. 19(1), pages 57-63, January.
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