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October 2005 On adaptive estimation of linear functionals
T. Tony Cai, Mark G. Low
Ann. Statist. 33(5): 2311-2343 (October 2005). DOI: 10.1214/009053605000000633


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.


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T. Tony Cai. Mark G. Low. "On adaptive estimation of linear functionals." Ann. Statist. 33 (5) 2311 - 2343, October 2005.


Published: October 2005
First available in Project Euclid: 25 November 2005

zbMATH: 1086.62031
MathSciNet: MR2211088
Digital Object Identifier: 10.1214/009053605000000633

Primary: 62G99
Secondary: 62F12 , 62F35 , 62M99

Keywords: adaptive estimation , between-class modulus of continuity , cost of adaptation , linear functional , ordered modulus of continuity , White noise model

Rights: Copyright © 2005 Institute of Mathematical Statistics


Vol.33 • No. 5 • October 2005
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