I've seen methods for maximizing Kendall's tau using regression with a single independent variable, e.g. Sen's 1968 article. I'm interested in fitting coefficients in a multiple linear regression that maximizes Kendall's tau (i.e. the case with multiple independent variables). Is this possible?
A related question is whether a multivariate Theil-Sen regression maximizes Kendall's tau?
(I know that Theil-Sen is based on Kendall's tau, but I'm not sure it is guaranteed to maximize it. If so, that would be the answer to the question. If not, I suspect there is not an elegant approach, and one would need to use brute force calculations.)