The Annals of Statistics
- Ann. Statist.
- Volume 34, Number 1 (2006), 202-228.
Adaptive confidence balls
Adaptive confidence balls are constructed for individual resolution levels as well as the entire mean vector in a multiresolution framework. Finite sample lower bounds are given for the minimum expected squared radius for confidence balls with a prespecified confidence level. The confidence balls are centered on adaptive estimators based on special local block thresholding rules. The radius is derived from an analysis of the loss of this adaptive estimator. In addition adaptive honest confidence balls are constructed which have guaranteed coverage probability over all of ℝN and expected squared radius adapting over a maximum range of Besov bodies.
Ann. Statist., Volume 34, Number 1 (2006), 202-228.
First available in Project Euclid: 2 May 2006
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G99: None of the above, but in this section
Secondary: 62F12: Asymptotic properties of estimators 62F35: Robustness and adaptive procedures 62M99: None of the above, but in this section
Cai, T. Tony; Low, Mark G. Adaptive confidence balls. Ann. Statist. 34 (2006), no. 1, 202--228. doi:10.1214/009053606000000146. https://projecteuclid.org/euclid.aos/1146576261