Adaptive confidence balls

Abstract

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 ${\mathbb{R}}^N$ and expected squared radius adapting over a maximum range of Besov bodies.

Published at http://dx.doi.org/10.1214/009053606000000146 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Adaptive nonparametric confidence sets
• Adaptive confidence balls
• Confidence sets for nonparametric wavelet regression
• Confidence balls in Gaussian regression

Cited by in corpus (15)

• Frequentist coverage of adaptive nonparametric Bayesian credible sets
• Confidence bands in density estimation
• A simple bootstrap method for constructing nonparametric confidence bands for functions
• Confidence sets in sparse regression
• On adaptive inference and confidence bands
• Adaptive nonparametric confidence sets
• Nonquadratic estimators of a quadratic functional
• Adaptive confidence balls
• Conditional predictive inference post model selection
• Minimax and Adaptive Inference in Nonparametric Function Estimation
• Testability of high-dimensional linear models with non-sparse structures
• Asymptotic equivalence and adaptive estimation for robust nonparametric regression
• Testing the regularity of a smooth signal
• Confidence regions and minimax rates in outlier-robust estimation on the probability simplex
• Honest confidence sets for high-dimensional regression by projection and shrinkage