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.Comment: Published 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
