Abstract
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.
Information
Published: 1 January 2009
First available in Project Euclid: 2 February 2010
zbMATH: 1243.62042
MathSciNet: MR2797956
Digital Object Identifier: 10.1214/09-IMSCOLL521
Subjects:
Primary:
60K35
,
60K35
Secondary:
60K35
Keywords:
Diffusion tensor imaging
,
integral curves
,
Nadaraya-Watson estimators
,
optimal convergence rates
Rights: Copyright © 2009, Institute of Mathematical Statistics
