Asymptotic normality and confidence intervals for inverse regression models with convolution-type operators

Abstract

We consider inverse regression models with convolution-type operators which mediate convolution on R^d (d ≥ 1) and prove a pointwise central limit theorem for spectral regularisation estimators which can be applied to construct pointwise confidence regions. Here, we cope with the unknown bias of such estimators by undersmoothing. Moreover, we prove consistency of the residual bootstrap in this setting and demonstrate the feasibility of the bootstrap confidence bands at moderate sample sizes in a simulation study.