The Annals of Statistics

Confidence balls in Gaussian regression

Yannick Baraud

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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.

Article information

Ann. Statist., Volume 32, Number 2 (2004), 528-551.

First available in Project Euclid: 28 April 2004

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G15: Tolerance and confidence regions
Secondary: 62G05: Estimation 62G10: Hypothesis testing

Confidence ball nonparametric regression hypothesis testing estimation


Baraud, Yannick. Confidence balls in Gaussian regression. Ann. Statist. 32 (2004), no. 2, 528--551. doi:10.1214/009053604000000085.

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