作者：Knapik, B. T.; van der Vaart, A. W.; van Zanten, J. H.
作者单位：Vrije Universiteit Amsterdam; Eindhoven University of Technology
摘要：The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothness and scale of the prior. Correct combinations of these characteristics lead to the minimax rate. The frequentist coverage of credible sets is shown to depend on the combination of prior and true parameter, with smoother priors leading to zero coverage and rougher priors to conservative coverage. In the latter case ...
作者：Dattner, I.; Goldenshluger, A.; Juditsky, A.
作者单位：University of Haifa; Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA)
摘要：The subject of this paper is the problem of nonparametric estimation of a continuous distribution function from observations with measurement errors. We study minimax complexity of this problem when unknown distribution has a density belonging to the Sobolev class, and the error density is ordinary smooth. We develop rate optimal estimators based on direct inversion of empirical characteristic function. We also derive minimax affine estimators of the distribution function which are given by an...
