Confidence balls in Gaussian regression

Details Confidence balls in Gaussian regression Confidence balls in Gaussian regression

2004-06-22

arxiv.org/abs/math/0406425v1

Annals of Statistics 2004, Vol. 32, No. 2, 528-551

Mathematics

Statistics Theory

Scientific paper

10.1214/009053604000000085

Starting from the observation of an R^n-Gaussian vector of mean f and
covariance matrix \sigma^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.

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