An Adaptation Theory For Nonparametric Confidence Intervals
The Annals of Statistics 32, 1805-1840, (2004).
An Adaptation Theory For Nonparametric Confidence Intervals
The Annals of Statistics 32, 1805-1840, (2004).
- 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.