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Selecting the length of a principal curve within a Gaussian model. (English) Zbl 1337.62074
Summary: 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.

62G08 Nonparametric regression and quantile regression
62G05 Nonparametric estimation
62H25 Factor analysis and principal components; correspondence analysis
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