Numerical issues in estimation of integral curves from noisy diffusion tensor data

The estimation of a diffusion tensor imaging (DTI) model proposed by Koltchinskii et al. (2007) involves two steps. The second step requires solving an ordinary differential equation, which in practice is solved by using a numerical approximation. We investigate how to balance the additional numerical error introduced by this approximation with the statistical estimation error using empirical mean integrated squared error for Euler’s and the second order Runge–Kutta approximations. We give practical guideline on how fast should the numerical approximation step grow with respect to the sample size.