Confidence balls in Gaussian regression
Yannick Baraud
Abstract
Starting from the observation of an Rn-Gaussian vector of mean f and covariance matrix σ2 In (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.
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