Confidence balls in Gaussian regression

Yannick Baraud

doi:10.1214/009053604000000085

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Home > Journals > Ann. Statist. > Volume 32 > Issue 2 > Article

April 2004 Confidence balls in Gaussian regression

Yannick Baraud

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Yannick Baraud¹
¹Département de Mathématiques et Applications, Ecole Normale Supérieure

Ann. Statist. 32(2): 528-551 (April 2004). DOI: 10.1214/009053604000000085

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Abstract

Starting from the observation of an ℝⁿ-Gaussian vector of mean f and covariance matrix σ²I_n (I_n 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.