Aaron Han (1987 in econometrics) proposed the Maximum Rank Correlation estimator that fits regression models by maximizing tau. Dougherty and Thomas (2012 in the psychology literature) recently proposed a very similar algorithm. There is an abundance of work on the MRC illustrating its properties.
Aaron K. Han, Non-parametric analysis of a generalized regression model: The maximum rank correlation estimator, Journal of Econometrics, Volume 35, Issues 2–3, July 1987, Pages 303-316, ISSN 0304-4076, http://dx.doi.org/10.1016/0304-4076(87)90030-3. (http://www.sciencedirect.com/science/article/pii/0304407687900303)
Dougherty, M. R., & Thomas, R. P. (2012). Robust decision making in a nonlinear world. Psychological review, 119 (2), 321. Retrieved from http://damlab.umd.edu/pdf%20articles/DoughertyThomas2012Rev.pdf.
