Integral curves of noisy vector fields and statistical problems in diffusion tensor imaging: nonparametric kernel estimation and hypotheses testing

Vladimir Koltchinskii, Lyudmila Sakhanenko, Songhe Cai

Let $v$ be a vector field in a bounded open set $G\subset {\mathbb{R}}^d$. Suppose that $v$ is observed with a random noise at random points $X_i,i=1,...,n,$ that are independent…