Abstract
The estimation of a star-shaped set S from a random sample of points X1,…,Xn ∊ S is considered. We show that S can be consistently approximated (with respect to both the Hausdorff metric and the ‘distance in measure’ between sets) by an estimator ŝn defined as a union of balls centered at the sample points with a common radius which can be chosen in such a way that ŝn is also star-shaped. We also prove that, under some mild conditions, the topological boundary of the estimator ŝn converges, in the Hausdorff sense, to that of S; this has a particular interest when the proposed estimation problem is considered from the point of view of statistical image analysis.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
