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Visual Error Criteria for Qualitative Smoothing

J. S. Marron and A. B. Tsybakov
Journal of the American Statistical Association
Vol. 90, No. 430 (Jun., 1995), pp. 499-507
DOI: 10.2307/2291060
Stable URL: http://www.jstor.org/stable/2291060
Page Count: 9
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Visual Error Criteria for Qualitative Smoothing
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Abstract

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.

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