Template-Type: ReDIF-Paper 1.0
Title: Invariant points of low dimensional curve families
Author-Name: Klaus J. Utikal
Classification-JEL: C13, C14, C21
Keywords: kernel smoothing, density estimation, principal component analysis, nonparametric functional prediction
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. 
Series:	Sonderforschungsbereich 303, University of Bonn, Germany
Length: 10 pages
Creation-Date: 1990-09
Handle: RePEc:bon:bonsfa:516