Scale space theory from computer vision leads to an interesting and
novel approach to nonparametric curve estimation. The family of smooth curve
estimates indexed by the smoothing parameter can be represented as a surface
called the scale space surface. The smoothing parameter here plays the
same role as that played by the scale of resolution in a visual system. In this
paper, we study in detail various features of that surface from a statistical
viewpoint. Weak convergence of the empirical scale space surface to its
theoretical counterpart and some related asymptotic results have been
established under appropriate regularity conditions. Our theoretical analysis
provides new insights into nonparametric smoothing procedures and yields useful
techniques for statistical exploration of features in the data. In particular,
we have used the scale space approach for the development of an effective
exploratory data analytic tool called SiZer.
Publié le : 2000-04-15
Classification:
Causality,
Gaussian kernel,
heat diffusion,
regression smoothers,
mode and anti-mode trees,
significance of zero crossings,
62G07
@article{1016218224,
author = {Chaudhuri, Probal and Marron, J. S.},
title = {Scale space view of curve estimation},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 408-428},
language = {en},
url = {http://dml.mathdoc.fr/item/1016218224}
}
Chaudhuri, Probal; Marron, J. S. Scale space view of curve estimation. Ann. Statist., Tome 28 (2000) no. 3, pp. 408-428. http://gdmltest.u-ga.fr/item/1016218224/