## The Annals of Statistics

### Confidence balls in Gaussian regression

Yannick Baraud

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 28 April 2004

Permanent link to this document
https://projecteuclid.org/euclid.aos/1083178937

Digital Object Identifier
doi:10.1214/009053604000000085

Mathematical Reviews number (MathSciNet)
MR2060168

Zentralblatt MATH identifier
1093.62051

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

#### Citation

Baraud, Yannick. Confidence balls in Gaussian regression. Ann. Statist. 32 (2004), no. 2, 528--551. doi:10.1214/009053604000000085. https://projecteuclid.org/euclid.aos/1083178937

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