Adaptive confidence balls

Adaptive confidence balls

Adaptive confidence balls are constructed for individual resolution levels as well as the entire mean vector in a multiresolution framework. Finite sample lower bounds are given for the minimum expected squared radius for confidence balls with a prespecified confidence level. The confidence balls are centered on adaptive estimators based on special local block thresholding rules. The radius is ...

Adaptive non-asymptotic confidence balls in density estimation

Confidence Balls in Gaussian Regression

where f = (f1, . . . , fn) ′ is an unknown vector, σ a positive number and ε1, . . . , εn a sequence of i.i.d. standard Gaussian random variables. For some β ∈ ]0,1[, the aim of this paper is to build a nonasymptotic Euclidean confidence ball for f with probability of coverage 1− β from the observation of Y = (Y1, . . . , Yn) ′. This statistical model includes, as a particular case, the functio...

Adaptive Confidence Bands

We show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions. We propose instead to construct adaptive bands that cover a surrogate function f which is close to, but simpler than, f . The surrogate captures the significant features in f . We establish lower bounds on the width for any confidence band for f and construct a procedure tha...

Adaptive Nonparametric Confidence Sets

We construct honest confidence regions for a Hilbert space-valued parameter in various statistical models. The confidence sets can be centered at arbitrary adaptive estimators, and have diameter which adapts optimally to a given selection of models. The latter adaptation is necessarily limited in scope. We review the notion of adaptive confidence regions, and relate the optimal rates of the dia...