Einbeck, Jochen and Zayed, Mohammad (2014) 'Some asymptotics for localized principal components and curves.', Communications in statistics - theory and methods., 43 (8). pp. 1736-1749.
Abstract
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.
| Item Type: | Article |
|---|---|
| Keywords: | Kernels, Mean shift, PCA, Local principal curves. |
| Full text: | (AM) Accepted Manuscript Download PDF (4667Kb) |
| Status: | Peer-reviewed |
| Publisher Web site: | http://dx.doi.org/10.1080/03610926.2012.673676 |
| Publisher statement: | This is an Author's Accepted Manuscript of an article published in Einbeck, Jochen and Zayed, Mohammad (2014) 'Some asymptotics for localized principal components and curves.', Communications in statistics - theory and methods., 43 (8). pp. 1736-1749. © Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/03610926.2012.673676. |
| Date accepted: | 05 March 2012 |
| Date deposited: | 16 April 2014 |
| Date of first online publication: | 12 August 2013 |
| Date first made open access: | No date available |
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