Conditional Extremes and Near-Extremes
MIT Dept. of Economics Working Paper No. 01-21
46 Pages Posted: 8 Jun 2001
Date Written: July 2000
Abstract
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) data. The applications, ranging from the analysis of babies' very low birth weights, (S,s) models, tail analysis in heteroscedastic regression models, outlier-robust inference in auction models, and decision-making under extreme uncertainty, provide the motivation and applications of this theory.
Keywords: Quantile regression, extreme value theory, tail analysis, (S,s) models, auctions, price search, Extreme Risk
JEL Classification: C13, C14, C21, C41, C51, C53, D21, D44, D81
Suggested Citation: Suggested Citation
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