Date of this Version
The Annals of Statistics
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.
adaptation, between class modulus, confidence intervals, coverage, expected length, linear functionals, minimax estimation, modulus of continuity, white noise model
Cai, T., & Low, M. G. (2004). An Adaptation Theory for Nonparametric Confidence Intervals. The Annals of Statistics, 32 (5), 1805-1840. http://dx.doi.org/10.1214/009053604000000049
Date Posted: 27 November 2017
This document has been peer reviewed.