SFB 303 Discussion Paper No. A - 516

Author: Utikal, Klaus J.
Title: Invariant points of low dimensional curve families
Abstract: From noisy observations of a finite family of functions an approximation in a lower dimensional space can be constructed using the method of principal components. If certain restrictions are to be satisfied by the approximation, e.g. being densities, this leads to a modified estimation procedure. It is shown that in certain dimensions this will produce a family of curves which all intersect in the same points. This property may be interpreted in some cases as a characteristic feature of regularity of the data or as an artificial creation by the device in others.
Keywords: kernel smoothing, density estimation, principal component analysis, nonparametric functional prediction
JEL-Classification-Number: C13, C14, C21
Creation-Date: February 1996
URL: ../1996/a/bonnsfa516.pdf

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