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2013 Selecting the length of a principal curve within a Gaussian model
Aurélie Fischer
Electron. J. Statist. 7: 342-363 (2013). DOI: 10.1214/13-EJS775


Principal curves are parameterized curves passing “through the middle” of a data cloud. These objects constitute a way of generalization of the notion of first principal component in Principal Component Analysis. Several definitions of principal curve have been proposed, one of which can be expressed as a least-square minimization problem. In the present paper, adopting this definition, we study a Gaussian model selection method for choosing the length of the principal curve, in order to avoid interpolation, and obtain a related oracle-type inequality. The proposed method is practically implemented and illustrated on cartography problems.


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Aurélie Fischer. "Selecting the length of a principal curve within a Gaussian model." Electron. J. Statist. 7 342 - 363, 2013.


Published: 2013
First available in Project Euclid: 28 January 2013

zbMATH: 1337.62074
MathSciNet: MR3020424
Digital Object Identifier: 10.1214/13-EJS775

Primary: 62G05, 62G08

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society


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