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Entropy 2016, 18(10), 375; doi:10.3390/e18100375

Non-Asymptotic Confidence Sets for Circular Means

Institut für Mathematik, Technische Universität Ilmenau, 98684 Ilmenau, Germany
This paper is an extended version of our paper published in Proceedings of the 2nd International Conference on Geometric Science of Information, Palaiseau, France, 28–30 October 2015; Nielsen, F., Barbaresco, F., Eds.; Lecture Notes in Computer Science, Volume 9389; Springer International Publishing: Cham, Switzerland, 2015; pp. 635–642.
These authors contributed equally to this work.
Author to whom correspondence should be addressed.
Academic Editors: Frédéric Barbaresco and Frank Nielsen
Received: 15 July 2016 / Revised: 10 October 2016 / Accepted: 13 October 2016 / Published: 20 October 2016
(This article belongs to the Special Issue Differential Geometrical Theory of Statistics)
View Full-Text   |   Download PDF [345 KB, uploaded 25 October 2016]   |  


The mean of data on the unit circle is defined as the minimizer of the average squared Euclidean distance to the data. Based on Hoeffding’s mass concentration inequalities, non-asymptotic confidence sets for circular means are constructed which are universal in the sense that they require no distributional assumptions. These are then compared with asymptotic confidence sets in simulations and for a real data set. View Full-Text
Keywords: directional data; circular mean; universal confidence sets; non-asymptotic confidence sets; mass concentration inequalities; Hoeffding’s inequality directional data; circular mean; universal confidence sets; non-asymptotic confidence sets; mass concentration inequalities; Hoeffding’s inequality

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Hotz, T.; Kelma, F.; Wieditz, J. Non-Asymptotic Confidence Sets for Circular Means. Entropy 2016, 18, 375.

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