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Quantile and probability curves without crossing

Authors: Victor Chernozhukov , Ivan Fernandez-Val and Alfred Galichon
Date: 31 May 2010
Type: Journal Article, Econometrica, Vol. 78, No. 3, pp. 1093–1125
DOI: 10.3982/ECTA7880

Abstract

The most common approach to estimating conditional quantile curves is to fit a curve, typically linear, pointwise for each quantile. Linear functional forms, coupled with pointwise fitting, are used for a number of reasons including parsimony of the resulting approximations and good computational properties. The resulting fits, however, may not respect a logical monotonicity requirement that the quantile curve be increasing as a function of probability. This paper studies the natural monotonization of these empirical curves induced by sampling from the estimated non-monotone model, and then taking the resulting conditional quantile curves that by construction are monotone in the probability.

Previous version:
Victor Chernozhukov, Ivan Fernandez-Val and Alfred Galichon April 2007, Quantile and probability curves without crossing, cemmap Working Paper, CWP10/07

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