Adaptation Under Probabilistic Error For Estimating Linear Functionals
Tony Cai and Mark Low
-
Abstract:
The problem of estimating linear functionals based on Gaussian
observations is considered. Probabilistic error is used as a measure
of accuracy and attention is focused on the construction of adaptive
estimators which are simultaneously near optimal under probabilistic
error over a collection of convex parameter spaces. In contrast to
mean squared error it is shown that fully rate optimal adaptive
estimators can be constructed for probabilistic error. A general
construction of such estimators is provided and examples are given to
illustrate the general theory.
- Paper:
pdf file.
- Other related papers:
Cai, T. & Low, M. (2004).
An adaptation theory for nonparametric confidence intervals.
The Annals of Statistics 32, 1805-1840.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.