Adaptive Estimation of Linear Functionals Under Different Performance Measures
Bernoulli 11, 341-358, (2005).
- Abstract: Lower bounds are given for probabilistic error subject to a mean squared error constraint. Consequences for the expected length of variable length confidence intervals centered on adaptive estimators are given. It is shown that in many contexts centering confidence intervals on adaptive estimators must lead either to poor coverage probability or unnecessarily long intervals.
- 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. (2004).
An adaptation theory for nonparametric confidence intervals.
The Annals of Statistics 32, 1805-1840.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.