The Annals of Statistics

On adaptive estimation of linear functionals

T. Tony Cai and Mark G. Low

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Abstract

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

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

Dates
First available in Project Euclid: 25 November 2005

Permanent link to this document
https://projecteuclid.org/euclid.aos/1132936565

Digital Object Identifier
doi:10.1214/009053605000000633

Mathematical Reviews number (MathSciNet)
MR2211088

Zentralblatt MATH identifier
1086.62031

Subjects
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

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

Citation

Cai, T. Tony; Low, Mark G. On adaptive estimation of linear functionals. Ann. Statist. 33 (2005), no. 5, 2311--2343. doi:10.1214/009053605000000633. https://projecteuclid.org/euclid.aos/1132936565


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