EXTREME VALUE THEORY WITH OPERATOR NORMING.
A new approach to extreme value theory is presented for vector data with heavy tails. The tail index is allowed to vary with direction, where the directions are not necessarily along the coordinate axes. Basic asymptotic theory is developed, using operator regular variation and extremal integrals. A test is proposed to judge whether the tail index varies with direction in any given data set.
Department of Statistics & Probability, Michigan State University, East Lansing MI 48824 USA. URL: http://www.stt.msu.edu/users/mcubed/
Mark M
MM
Meerschaert
Fachbereich Mathematik, Universität Siegen, 57068 Siegen, Germany, URL: http://www.uni-siegen.de/fb6/src/scheffler/
Hans-Peter
HP
Scheffler
Department of Statistics, University of Michigan, Ann Arbor, MI 48109, URL: http://www.stat.lsa.umich.edu/~sstoev.
Stilian A
SA
Stoev
directional extremes; heavy tails; hetero-ouracity; operator regular variation; parametric bootstrap; spectral representation