An adaptation theory for nonparametric confidence intervals

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.

arXiv commentPublished at http://dx.doi.org/10.1214/009053604000000049 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (2)

• Confidence sets for nonparametric wavelet regression
• Minimax estimation of linear functionals over nonconvex parameter spaces

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