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Conditional extremes and near-extremes

by Victor Chernozhukov

This paper develops a theory of high and low (extremal) quantile regression: the linear models, estimation, and inference. In particular, the models coherently combine the convenient, flexible linearity with the extreme-value-theoretic restrictions on tails and the general heteroscedasticity forms. Within these models, the limit laws for extremal quantile regression statistics are obtained under the rank conditions (experiments) constructed to reflect the extremal or rare nature of tail events. An inference framework is discussed. The results apply to cross-section (and possibly dependent)...

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