An adaptation theory for nonparametric confidence intervals

Details An adaptation theory for nonparametric confidence intervals An adaptation theory for nonparametric confidence intervals

2005-03-29

arxiv.org/abs/math/0503662v1

Annals of Statistics 2004, Vol. 32, No. 5, 1805-1840

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053604000000049 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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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