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Scale space view of curve estimation. (English) Zbl 1106.62318

Summary: 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.

MSC:

62G07 Density estimation
62H35 Image analysis in multivariate analysis
62G05 Nonparametric estimation

Software:

SiZer ; KernSmooth
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Full Text: DOI Euclid

References:

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