B0727
Title: Partial tail correlation for extremes
Authors: Jeongjin Lee - University of Namur (Belgium) [presenting]
Abstract: A method is developed for investigating conditional extremal relationships between pairs of variables. We consider an inner product space constructed from transformed-linear combinations of independent regularly varying random variables. By developing the projection theorem for the inner product space, we derive the concept of partial tail correlation via the projection theorem. We show that the partial tail correlation can be understood as the inner product of the prediction errors associated with the transformed linear prediction. Similar to Gaussian cases, we connect the partial tail correlation to the inverse of the inner product matrix and show that a zero in this inverse implies a partial tail correlation of zero. We develop a hypothesis test for the partial tail correlation of zero and demonstrate the performance in a simulation study as well as in two applications: extreme river discharges in the upper Danube basin and high nitrogen dioxide levels in Washington DC.
