A GLOBAL OPTIMAL CONVERGENCE RATE IN A MODEL FOR THE DIFFUSION TENSOR IMAGING

In their recent work Koltchinskii, Sakhanenko, and Cai [Ann. Statist., 35 (2007), pp. 1576-1607] proposed and studied estimators for integral curves based on noisy data of the corresponding gradient vector field. That estimation problem was motivated by diffusion tensor imaging, a popular brain imaging technique. Recently Sakhanenko [Theory Probab. Appl., 54 (2009), pp. 166-177] showed that those estimates have pointwise optimal convergence rate in a minimax sense. In this work we show that these estimators are convergence rate-optimal in the minimax sense with respect to the integral L-p-norm, 1 <= p <= infinity. This result closes up a gap in the research on the optimal convergence rates for these estimators.