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EXTREME VALUE THEORY WITH OPERATOR NORMING.

ABSTRACT: 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.

SUBMITTER: Meerschaert MM 

PROVIDER: S-EPMC3892951 | biostudies-other | 2013 Dec

REPOSITORIES: biostudies-other

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EXTREME VALUE THEORY WITH OPERATOR NORMING.

Meerschaert Mark M MM   Scheffler Hans-Peter HP   Stoev Stilian A SA  

Extremes 20131201 4

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. ...[more]

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