Confidence balls in Gaussian regression
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Open Access
- 1 April 2004
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 32 (2) , 528-551
Abstract
Starting from the observation of an ℝn-Gaussian vector of mean f and covariance matrix σ2In (In is the identity matrix), we propose a method for building a Euclidean confidence ball around f, with prescribed probability of coverage. For each n, we describe its nonasymptotic property and show its optimality with respect to some criteria.Keywords
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This publication has 6 references indexed in Scilit:
- Random rates in anisotropic regression (with a discussion and a rejoinder by the authors)The Annals of Statistics, 2002
- An alternative point of view on Lepski's method2001
- Modulation of estimators and confidence setsThe Annals of Statistics, 1998
- Confidence sets centered at C p -estimatorsAnnals of the Institute of Statistical Mathematics, 1996
- An Analysis of Bayesian Inference for Nonparametric RegressionThe Annals of Statistics, 1993
- Honest Confidence Regions for Nonparametric RegressionThe Annals of Statistics, 1989