# Multiple regression to maximize Kendall's tau

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.)

• Could you give references to the univariate cases you cite? How would Kendall's tau be defined for multiple predictors anyway? Can you give a little more context about what you're trying to achieve? – Ben Bolker Jul 10 '18 at 19:44
• A description of how this can be done in the univariate case is found in "Estimates of the Regression Coefficient Based on Kendall's Tau" (Pranab Kumar Sen, 1968 -- jstor.org/stable/2285891?seq=1#page_scan_tab_contents) – LittleUrsus Jul 10 '18 at 19:57
• And to the second question on defining Kendall's tau/more context, the goal is to maximize Kendall's tau between the fitted regression (let's call it Y where Y is the linear combination of a set of independent variables Xi, i.e. Y=b0+b1*X1+..+bp*Xp) and another variable, call it Z. The idea would be using Y (the linear combination of X-variables) as a predictor for Z. – LittleUrsus Jul 10 '18 at 20:04
• Please put the link and any additional relevant information in your question (via an edit). Note that we have many questions on site relating to Theil-Sen regression – Glen_b Jul 11 '18 at 3:05