# 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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