Prof. I. Gijbels (KU Leuven, Netherlands)
Wednesday, June 16, 2021 - 12:30
Online Event
Der Vortrag findet bei Zoom statt:, --- ---
Forschungsseminar Mathematische Statistik
Quantiles and expectiles of a distribution are found to be useful descriptors of its tail in the same way as the median and mean are related to its central behavior. In this talk we discuss an alternative class to expectiles, called extremiles. The new class is motivated via several angles, which reveals its speci c merits and strengths. Extremiles suggest better capability of tting both location and spread in data points and provide an appropriate theory that better displays the interesting features of long-tailed distributions. We brie y discuss estimation of extremiles. A large part of the talk will be on regression extremiles, which thus de ne a least squares analogue of regression quantiles.We discuss estimation of conditional extremiles, in which we rely on local linear (least squares) checkfunction minimization. An asymptotic normality result for the estimators is established. Attention also goes to extending extremile regression far into the tails of heavy-tailed distributions. For this purpose extrapolated estimators are constructed and their asymptotic theory is developed. Applications to real data illustrate how extremiles and related tools can be used in practice.)
submitted by chschnei (, 030 20372574)