The Institute for Statistics and Mathematics is pleased to invite you to the next research seminar, taking place on campus:

Marc-Oliver Pohle (Faculty of Economics and Business, Goethe University Frankfurt)
Generalised Covariances and Correlations
Friday, December 2, 2022, 10:30 am, Building TC, Room TC.3.01

Abstract:
We introduce and examine new dependence measures. Generalised covariance and correlation allow to measure dependence between two random variables X and Y around arbitrary statistical functionals just as covariance and Pearson correlation measures dependence around their means. The key idea behind this is to replace the error or deviation from the mean showing up in Pearson correlation by a suitable measure for the deviation from a general statistical functional, where identification functions provide us with such a generalized error. Generalised correlation has favourable theoretical properties and a multitude of practically relevant measures arise from this class, for example quantile correlation. Quantile correlation is akin to the extension of least squares to quantile regression. Quantile and the related threshold correlation make it possible to measure dependence locally, for example to analyse tail dependence. When choosing distribution functions as functionals we arrive at distributional correlations, which are two-dimensional functions lying between -1 and 1. They uncover the full dependence structure between X and Y and are closely related as well as natural complements in statistical analysis to the joint CDF and the copula. To condense the full dependence structure into a single number we finally introduce summary correlations as appropriately normalized integrals over distributional covariances with respect to arbitrary measures. Interesting new measures arise, but also Spearman's rho and an improved version of Pearson correlation as canonical special cases.

Joint work with Tobias Fissler.

We aim to stream all on-campus talks via Zoom. A direct link to the stream will be posted on our website.

For further information and the seminar schedule, please see:
www.wu.ac.at/en/statmath/research/resseminar