We report an error in Theorem 4.1 of the paper identified in the title. That theorem is not true in general. However, the main mathematical message in the paper as well as all subsidiary mathematical remarks and all simulations and numerical results are correct. As the title suggests, the paper concerns successive normalization of rectangular arrays. We learned the algorithm from Bradley Efron. Here we sketch the algorithm, state the mistake in our paper, sketch our approach to proving its main theorem, and give reference to a paper by the authors where many more details can be found.
"Correction: Successive normalization of rectangular arrays." Ann. Statist. 41 (5) 2700 - 2702, October 2013. https://doi.org/10.1214/13-AOS1177