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Chernozhukov, Victor
Fernández-Val, Iván
Galichon, Alfred
Year of Publication: 
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cemmap working paper, Centre for Microdata Methods and Practice CWP10/07
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.
Quantile regression , Monotonicity , Rearrangement , Approximation , Functional Delta Method , Hadamard Differentiability of Rearrangement Operators
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Working Paper

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