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.
"Confidence balls in Gaussian regression." Ann. Statist. 32 (2) 528 - 551, April 2004. https://doi.org/10.1214/009053604000000085