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October 2004 An adaptation theory for nonparametric confidence intervals
T. Tony Cai, Mark G. Low
Ann. Statist. 32(5): 1805-1840 (October 2004). DOI: 10.1214/009053604000000049


A nonparametric adaptation theory is developed for the construction of confidence intervals for linear functionals. A between class modulus of continuity captures the expected length of adaptive confidence intervals. Sharp lower bounds are given for the expected length and an ordered modulus of continuity is used to construct adaptive confidence procedures which are within a constant factor of the lower bounds. In addition, minimax theory over nonconvex parameter spaces is developed.


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T. Tony Cai. Mark G. Low. "An adaptation theory for nonparametric confidence intervals." Ann. Statist. 32 (5) 1805 - 1840, October 2004.


Published: October 2004
First available in Project Euclid: 27 October 2004

zbMATH: 1056.62060
MathSciNet: MR2102494
Digital Object Identifier: 10.1214/009053604000000049

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

Keywords: Adaptation , between class modulus , confidence intervals , coverage , expected length , linear functionals , minimax estimation , modulus of continuity , White noise model

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.32 • No. 5 • October 2004
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