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VOL. 5 | 2009 Asymptotics of statistical estimators of integral curves
Vladimir Koltchinskii, Lyudmila Sakhanenko

Editor(s) Christian Houdré, Vladimir Koltchinskii, David M. Mason, Magda Peligrad


The problem of estimation of integral curves of a vector field based on its noisy observations is studied. For Nadaraya-Watson type estimators, several results on asymptotics of the shortest distance from the estimated curve to a specified region have been proved. The problem is motivated by applications in diffusion tensor imaging where it is of importance to test various hypotheses of geometric nature based on the estimated distances.


Published: 1 January 2009
First available in Project Euclid: 2 February 2010

zbMATH: 1243.62042
MathSciNet: MR2797956

Digital Object Identifier: 10.1214/09-IMSCOLL521

Primary: 60K35 , 60K35
Secondary: 60K35

Keywords: Diffusion tensor imaging , integral curves , Nadaraya-Watson estimators , optimal convergence rates

Rights: Copyright © 2009, Institute of Mathematical Statistics


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