Rolling-ball method for estimating the boundary of the support of a point-process intensity |
| |
Authors: | Peter Hall Byeong U Park Berwin A Turlach |
| |
Affiliation: | a Centre for Mathematics and its Applications, Australian National University, Canberra, ACT 0200, Australia;b Department of Statistics, Seoul National University, Seoul 151-742, South Korea;c Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia |
| |
Abstract: | We suggest a generalisation of the convex-hull method, or ‘DEA’ approach, for estimating the boundary or frontier of the support of a point cloud. Figuratively, our method involves rolling a ball around the cloud, and using the equilibrium positions of the ball to define an estimator of the envelope of the point cloud. Constructively, we use these ideas to remove lines from a triangulation of the points, and thereby compute a generalised form of a convex hull. The radius of the ball acts as a smoothing parameter, with the convex-hull estimator being obtained by taking the radius to be infinite. Unlike the convex-hull approach, however, our method applies to quite general frontiers, which may be neither convex nor concave. It brings to these contexts the attractive features of the convex hull: simplicity of concept, rotation-invariance, and ready extension to higher dimensions. It admits bias corrections, which we describe and illustrate through implementation. |
| |
Keywords: | Bias correction Confidence band Curvature Envelope Frontier Productivity analysis Rotation invariance |
本文献已被 ScienceDirect 等数据库收录! |
|