A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf
.
Estimating the reach of a manifold
2019
Electronic Journal of Statistics
Various problems in manifold estimation make use of a quantity called the reach, denoted by τ M , which is a measure of the regularity of the manifold. This paper is the first investigation into the problem of how to estimate the reach. First, we study the geometry of the reach through an approximation perspective. We derive new geometric results on the reach for submanifolds without boundary. An estimatorτ of τ M is proposed in a framework where tangent spaces are known, and bounds assessing
doi:10.1214/19-ejs1551
fatcat:6oaoefebqjfmflb7la5645ixly