An adaptation theory for nonparametric confidence intervals
T. Tony Cai and Mark G. Low
Source: Ann. Statist. Volume 32, Number 5 (2004), 1805-1840.
Abstract
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.
Primary Subjects: 62G99
Secondary Subjects: 62F12, 62F35, 62M99
Keywords: Adaptation; between class modulus; confidence intervals; coverage; expected length; linear functionals; minimax estimation; modulus of continuity; white noise model
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.aos/1098883773
Digital Object Identifier: doi:10.1214/009053604000000049
Mathematical Reviews number (MathSciNet):
MR2102494
Zentralblatt MATH identifier:
1056.62060
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