作者：Berrett, Thomas B.; Samworth, Richard J.; Yuan, Ming
作者单位：University of Cambridge; University of Wisconsin System; University of Wisconsin Madison
摘要：Many statistical procedures, including goodness-of-fit tests and methods for independent component analysis, rely critically on the estimation of the entropy of a distribution. In this paper, we seek entropy estimators that are efficient and achieve the local asymptotic minimax lower bound with respect to squared error loss. To this end, we study weighted averages of the estimators originally proposed by Kozachenko and Leonenko [Probl. Inform. Transm. 23 (1987), 95-101], based on the k-nearest...
作者：Patschkowski, Tim; Rohde, Angelika
作者单位：Ruhr University Bochum; University of Freiburg
摘要：We develop honest and locally adaptive confidence bands for probability densities. They provide substantially improved confidence statements in case of inhomogeneous smoothness, and are easily implemented and visualized. The article contributes conceptual work on locally adaptive inference as a straightforward modification of the global setting imposes severe obstacles for statistical purposes. Among others, we introduce a statistical notion of local Holder regularity and prove a corresponding...
