The Annals of Statistics
- Ann. Statist.
- Volume 28, Number 2 (2000), 408-428.
Scale space view of curve estimation
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.
Ann. Statist., Volume 28, Number 2 (2000), 408-428.
First available in Project Euclid: 15 March 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62G07: Density estimation
Chaudhuri, Probal; Marron, J. S. Scale space view of curve estimation. Ann. Statist. 28 (2000), no. 2, 408--428. doi:10.1214/aos/1016218224. https://projecteuclid.org/euclid.aos/1016218224