A class of estimators of the Rényi and Tsallis entropies of an unknown distribution f in R m is presented. These estimators are based on the kth nearest-neighbor distances computed from a sample of N i.i.d. vectors with distribution f . We show that entropies of any order q, including Shannon's entropy, can be estimated consistently with minimal assumptions on f . Moreover, we show that it is straightforward to extend the nearest-neighbor method to estimate the statistical distance between two distributions using one i.i.d. sample from each.
International audienceWhen setting up a computer experiment, it has become a standard practice to select the inputs spread out uniformly across the available space. These so-called space-filling designs are now ubiquitous in corresponding publications and conferences. The statistical folklore is that such designs have superior properties when it comes to prediction and estimation of emulator functions. In this paper we want to review the circumstances under which this superiority holds, provide some new arguments and clarify the motives to go beyond space-filling. An overview over the state of the art of space-filling is introducing and complementing these results
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.