B0617
Title: Asymptotic theory for density ridges
Authors: Yen-Chi Chen - University of Washington (United States) [presenting]
Abstract: The large sample theory of estimators for density modes is well-understood. We consider density ridges, which are a higher-dimensional extension of modes. Modes correspond to zero-dimensional, local high-density regions in point clouds. Density ridges correspond to $s-$dimensional, local high-density regions in point clouds. We derive geometric properties for density ridges and study asymptotic behavior for ridge estimators. We propose a valid procedure for constructing a confidence set for density ridges using the bootstrap.
