Some asymptotics for localized principal components and curves

Einbeck, Jochen; Zayed, Mohammad

doi:10.1080/03610926.2012.673676

Some asymptotics for localized principal components and curves

Einbeck, Jochen; Zayed, Mohammad

Authors

Professor Jochen Einbeck jochen.einbeck@durham.ac.uk
Professor

Mohammad Zayed

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.

Citation

Einbeck, J., & Zayed, M. (2014). Some asymptotics for localized principal components and curves. Communications in Statistics - Theory and Methods, 43(8), 1736-1749. https://doi.org/10.1080/03610926.2012.673676

Journal Article Type	Article
Acceptance Date	Mar 5, 2012
Online Publication Date	Aug 12, 2013
Publication Date	Apr 9, 2014
Deposit Date	Sep 13, 2013
Publicly Available Date	Apr 16, 2014
Journal	Communications in Statistics - Theory and Methods
Print ISSN	0361-0926
Electronic ISSN	1532-415X
Publisher	Taylor and Francis Group
Peer Reviewed	Peer Reviewed
Volume	43
Issue	8
Pages	1736-1749
DOI	https://doi.org/10.1080/03610926.2012.673676
Keywords	Kernels, Mean shift, PCA, Local principal curves.

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Copyright 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.