Publication detailsEinbeck, Jochen & Zayed, Mohammad (2014). Some asymptotics for localized principal components and curves. Communications in Statistics - Theory and Methods 43(8): 1736-1749.
- Publication type: Journal Article
- ISSN/ISBN: 0361-0926 (print), 1532-415X (electronic)
- DOI: 10.1080/03610926.2012.673676
- Keywords: Kernels, Mean shift, PCA, Local principal curves.
- Further publication details on publisher web site
- Durham Research Online (DRO) - may include full text
Author(s) from Durham
The asymptotic behavior of localized principal components applying kernels as weights is investigated. In particular, we show that the first-order approximation of the first localized principal component at any given point only depends on the bandwidth parameter(s) and the density at that point. This result is extended to the context of local principal curves, where the characteristics of the points at which the curve stops at the edges are identified. This is used to provide a method which allows the curve to proceed beyond its natural endpoint if desired.