Lower Bounds for Accuracy of Estimation in High Angular Resolution Diffusion Imaging Data

• Activity Number: 33 - Statistical Methods in Public Health Research
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Chitrak Banerjee* and Lyudmila Sakhanenko
• Companies: Michigan State University and Michigan State University
• Keywords: local asymptotic normality; optimal rate of convergence; high angular resolution diffusion imaging; nonparametric estimation

Abstract

High angular resonance diffusion imaging (HARDI) is a popular in vivo neuroimaging technique. A high order tensor model was developed by Özarslan and Mareci (2003) to model HARDI data. Sakhanenko (2012) established the minimax lower bounds for the asymptotic risk of the estimators of the integral curves under a simpler model with imaging signal modeled with vector field perturbed by an additive noise. Carmichael and Sakhanenko (2015) (C-S) investigated estimators of the integral curves and their asymptotic distributions with a proper rate of convergence in high order tensor models for HARDI. The present work seeks to establish the rate of convergence in the C-S paper is optimal in the minimax sense for the fiber estimators under a tensor model for the imaging signals. It also establishes the minimax lower bound for the asymptotic risk of the integral curve estimators under the tensor model, thereby extending the work of Sakhanenko (2012).