Non-parametric confidence bands in deconvolution density estimation

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...

Uniform Confidence Bands in Deconvolution with Unknown Error Distribution

This paper develops a method to construct confidence bands in deconvolution when the error distribution is unknown. We work with the case where an auxiliary sample from the error distribution is available and the error density is ordinary smooth. The construction is based upon the “intermediate” Gaussian approximation and the Gaussian multiplier bootstrap, but not on explicit limit distribution...

Density estimation with non–parametric methods

One key issue in several astrophysical problems is the evaluation of the density probability function underlying an observational discrete data set. We here review two non-parametric density estimators which recently appeared in the astrophysical literature, namely the adaptive kernel density estimator and the Maximum Penalized Likelihood technique, and describe another method based on the wave...

Adaptive non-asymptotic confidence balls in density estimation

Global confidence regions in parametric shape estimation

We introduce confidence region techniques for analyzing and visualizing the performance of two-dimensional parametric shape estimators. Assuming an asymptotically normal and efficient estimator for a finite parameterization of the object boundary, Cramér-Rao bounds are used to define a confidence region, centered around the true boundary. Computation of the probability that an entire boundary e...