Conference Agenda

In multivariate regression analysis, the multiple linear correlation coefficient is a commonly used association measure. This measure focuses on a linear relationship between a response variable and predictor variables. When moving away from the linearity of the functional relationship, then we arrive at Kendall's tau and multivariate versions, among others. In an earlier paper by the author (2021), the Kendall regression coefficient was introduced. Here, we extend the coefficient to vector responses Y and discuss properties of it. The coefficient we introduce describes to what degree the response variable Y can be approximated by a monotonous function of the regressors. These regressors are combined in a random vector. One advantage of this approach is that the association measure is based only on the copula (does not depend on marginal distributions), and is hence robust against outliers.
In the talk, we provide a series of interesting properties of the new Kendall coefficient, which are based on those described in Schmid et al. (2010). It turns out that it makes sense to consider Kendall coefficients w.r.t. the various directions of the regressors. Furthermore, we introduce an estimator for the Kendall coefficient, for which a central limit theorem is provided. It is demonstrated that the multivariate extension of Kendall's tau coefficients can be employed in multiple non-linear regression analysis and in dependence modelling, even in the situation of higher dimensions.
Literature:
Schmid, F.; Schmidt, R.; Blumentritt, T.; Gaißer, S.; Ruppert, M. (2010). Copula-based measures of multivariate association. in F. Durante, W. Härdle, P. Jaworski, T. Rychlik (eds.) Copula Theory and Its Applications. Springer Berlin, 2010.
Liebscher, E. (2021). Kendall regression coefficient. Computational Statistics and Data Analysis 157. 107140