The Annals of Statistics

Confidence balls in Gaussian regression

Yannick Baraud

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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

Keywords
Confidence ball nonparametric regression hypothesis testing estimation

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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References

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