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LEADER: 03859nam 2200421Ia 4500
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035 $a(OCoLC)137295885
040 $aMYG$cMYG
090 $aHB31.M415 no.07-15
100 1 $aChernozhukov, Victor.
245 10 $aQuantile and probability curves without crossing /$cby Victor Chernozhukov, Ivǹ Fernǹdez-Val [and] Alfred Galichon.
260 $aCambridge, MA :$bMassachusetts Institute of Technology, Dept. of Economics,$c[2007]
300 $a36 p.$bill. ;$c28 cm.
490 1 $aWorking paper series / Massachusetts Institute of Technology, Dept. of Economics ;$vworking paper 07-15
500 $a"April 27, 2007."
504 $aIncludes bibliographical references (p. 34-36).
520 3 $aThe 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. This construction of monotone quantile curves may be seen as a bootstrap and also as a monotonic rearrangement of the original non-monotone function. It is shown that the monotonized curves are closer to the true curves in finite samples, for any sample size. Under correct specification, the rearranged conditional quantile curves have the same asymptotic distribution as the original non-monotone curves. Under misspecification, however, the asymptotics of the rearranged curves may partially differ from the asymptotics of the original non-monotone curves.
520 3 $a(cont.) An analogous procedure is developed to monotonize the estimates of conditional distribution functions. The results are derived by establishing the compact (Hadamard) differentiability of the monotonized quantile and probability curves with respect to the original curves in discontinuous directions, tangentially to a set of continuous functions. In doing so, the compact differentiability of the rearrangement-related operators is established. Keywords: Quantile regression, Monotonicity, Rearrangement, Approximation, Functional Delta Method, Hadamard Differentiability of Rearrangement Operators. JEL Classifications: Primary 62J02; Secondary 62E20, 62P20.
530 $aAbstract in HTML and working paper for download in PDF available via World Wide Web at the Social Science Research Network.
700 1 $aFernǹdez-Val, Ivǹ.
700 1 $aGalichon, Alfred.
710 2 $aMassachusetts Institute of Technology.$bDept. of Economics.
830 0 $aWorking paper (Massachusetts Institute of Technology. Dept. of Economics) ;$vno. 07-15.
856 41 $uhttp://papers.ssrn.com/sol3/papers.cfm?abstract%5Fid=983158$zTo download paper, go to the abstract page choose a download option.
852 0 $bARC$cNOLN2$hHB31.M415 no.07-15$4Institute Archives$5Noncirculating Collection 2
852 0 $bDEW$cSTACK$hHB31.M415 no.07-15$4Dewey Library$5Stacks
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