Visual Error Criteria for Qualitative Smoothing

An important gap, between the classical mathematical theory and the practice and implementation of nonparametric curve estimation, is due to the fact that the usual norms on function spaces measure something different from what the eye can see visually in a graphical presentation. Mathematical error...

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Bibliographic Details
Published in:Journal of the American Statistical Association 1995-06, Vol.90 (430), p.499-507
Main Authors: Marron, J. S., Tsybakov, A. B.
Format: Article
Language:English
Subjects:
Approximation
Bandwidth selection
Curves
Data analysis
Data smoothing
Density estimation
Estimation methods
Estimation theory
Estimators
Exact sciences and technology
Eyes
Function spaces
Graphs
Mathematics
Nonparametric curve estimation
Nonparametric inference
Probability and statistics
Sciences and techniques of general use
Statistical methods
Statistics
Theory and Methods
Wavelet regression
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Description
Summary:An important gap, between the classical mathematical theory and the practice and implementation of nonparametric curve estimation, is due to the fact that the usual norms on function spaces measure something different from what the eye can see visually in a graphical presentation. Mathematical error criteria that more closely follow "visual impression" are developed and analyzed from both graphical and mathematical viewpoints. Examples from wavelet regression and kernel density estimation are considered.
ISSN:0162-1459
1537-274X
DOI:10.1080/01621459.1995.10476541