Adaptive non-asymptotic confidence balls in density estimation

Adaptive non-asymptotic confidence balls in density estimation

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 ...

Non-asymptotic bounds for prediction problems and 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...

Nonparametric confidence bands in deconvolution density estimation

Uniform confidence bands for densities f via nonparametric kernel estimates were first constructed by Bickel and Rosenblatt [Ann. Statist. 1, 1071–1095]. In this paper this is extended to confidence bands in the deconvolution problem g = f ∗ ψ for an ordinary smooth error density ψ. Under certain regularity conditions, we obtain asymptotic uniform confidence bands based on the asymptotic distri...