The Annals of Statistics

On adaptive estimation of linear functionals

T. Tony Cai and Mark G. Low

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Adaptive estimation of linear functionals over a collection of parameter spaces is considered. A between-class modulus of continuity, a geometric quantity, is shown to be instrumental in characterizing the degree of adaptability over two parameter spaces in the same way that the usual modulus of continuity captures the minimax difficulty of estimation over a single parameter space. A general construction of optimally adaptive estimators based on an ordered modulus of continuity is given. The results are complemented by several illustrative examples.

Article information

Ann. Statist., Volume 33, Number 5 (2005), 2311-2343.

First available in Project Euclid: 25 November 2005

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Zentralblatt MATH identifier

Primary: 62G99: None of the above, but in this section
Secondary: 62F12: Asymptotic properties of estimators 62F35: Robustness and adaptive procedures 62M99: None of the above, but in this section

Adaptive estimation between-class modulus of continuity cost of adaptation linear functional ordered modulus of continuity white noise model


Cai, T. Tony; Low, Mark G. On adaptive estimation of linear functionals. Ann. Statist. 33 (2005), no. 5, 2311--2343. doi:10.1214/009053605000000633.

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