SPEAKER: Professor Peter J. Rousseeuw

TITLE: Depth Tests of Symmetry and Regression

ABSTRACT: The halfspace location depth can be used to test whether the center of angular symmetry of a multivariate distribution equals a given point. When the point is not given in advance, we can test whether the distribution is angularly symmetric. Analogously, in the case of multiple regression (where $x$ is multivariate and $y$ is univariate) the regression depth can be used to test whether a distribution on $(x,y)$ has a conditional median equal to a given linear funtion of $x$. When the linear function is not given, we can test whether the conditional median of the distribution is linear.