An Adaptation Theory For Nonparametric Confidence Intervals
Tony Cai and Mark Low
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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.
- Paper:
pdf file.
- Other related papers:
Cai, T. & Low, M. (2004).
Minimax estimation of linear functionals over nonconvex parameter spaces.
The Annals of Statistics 32, 552 - 576.Cai, T. & Low, M. (2005).
Adaptive estimation of linear functionals under different performance measures.
Bernoulli 11, 1-18.Cai, T. & Low, M. (2005).
On adaptive estimation of linear functionals.
The Annals of Statistics 33, 2311-2343.Cai, T. & Low, M. (2006).
Adaptation under probabilistic error for estimating linear functionals.
J. Multivariate Analysis 97, 231-245.