Conditional Extremes and Near-Extremes

MIT Dept. of Economics Working Paper No. 01-21

46 Pages Posted: 8 Jun 2001

See all articles by Victor Chernozhukov

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics

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

Chernozhukov, Victor, Conditional Extremes and Near-Extremes (July 2000). MIT Dept. of Economics Working Paper No. 01-21, Available at SSRN: https://ssrn.com/abstract=272836 or http://dx.doi.org/10.2139/ssrn.272836

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