Confidence balls in Gaussian regression

Abstract

Starting from the observation of an ℝ n-Gaussian vector of mean f and covariance matrix σ 2 I 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. © Institute of Mathematical Statistics, 2004.