The Annals of Statistics

An adaptation theory for nonparametric confidence intervals

T. Tony Cai and Mark G. Low

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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.

Article information

Ann. Statist., Volume 32, Number 5 (2004), 1805-1840.

First available in Project Euclid: 27 October 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Adaptation between class modulus confidence intervals coverage expected length linear functionals minimax estimation modulus of continuity white noise model


Cai, T. Tony; Low, Mark G. An adaptation theory for nonparametric confidence intervals. Ann. Statist. 32 (2004), no. 5, 1805--1840. doi:10.1214/009053604000000049.

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