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Some asymptotics for localized principal components and curves.

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
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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.
Record Created:15 Apr 2014 16:05
Last Modified:12 Apr 2015 00:30

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