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April 2000 Scale space view of curve estimation
Probal Chaudhuri, J. S. Marron
Ann. Statist. 28(2): 408-428 (April 2000). DOI: 10.1214/aos/1016218224

Abstract

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.

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Probal Chaudhuri. J. S. Marron. "Scale space view of curve estimation." Ann. Statist. 28 (2) 408 - 428, April 2000. https://doi.org/10.1214/aos/1016218224

Information

Published: April 2000
First available in Project Euclid: 15 March 2002

zbMATH: 1106.62318
MathSciNet: MR1790003
Digital Object Identifier: 10.1214/aos/1016218224

Subjects:
Primary: 62G07

Keywords: causality , Gaussian kernel , heat diffusion , mode and anti-mode trees , regression smoothers , significance of zero crossings

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 2 • April 2000
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