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Carlier, Guillaume
Chernozhukov, Victor
Galichon, Alfred
Year of Publication: 
Series/Report no.: 
cemmap working paper, Centre for Microdata Methods and Practice CWP58/15
We propose a notion of conditional vector quantile function and a vector quantile regression. A conditional vector quantile function (CVQF) of a random vector Y, taking values in Rd given covariates Z=z, taking values in Rk, is a map u
Vector quantile regression
vector conditional quantile function
> QY(u,z), which is monotone, in the sense of being a gradient of a convex function, and such that given that vector U follows a reference non-atomic distribution FU, for instance uniform distribution on a unit cube in Rd, the random vector QY(U,z) has the distribution of Y conditional on Z=z. Moreover, we have a strong representation, Y =QY(U,Z) almost surely, for some version of U. The vector quantile regression (VQR) is a linear model for CVQF of Y given Z. Under correct specification, the notion produces strong representation,Y=ß(U)Tf(Z),for f(Z) denoting a known set of transformations of Z, where u
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Working Paper

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