Given a stepfunction Q(u), not necessarily monotone, let
F(y) = int { Q(u) ≤ y } du denote the associated cdf
obtained by randomly evaluating Q at U sim U[0,1]. The
rearranged version of Q is \tilde Q (u) = inf {
u: F(y) ≥ u }. The rearranged function inherits the right
or left continuity of original stepfunction.
Value
Produces transformed stepfunction that is monotonic increasing.
Author(s)
R. Koenker
References
Chernozhukov, V., I. Fernandez-Val, and A. Galichon, (2006) Quantile and Probability
Curves without Crossing, Econometrica, forthcoming.
Chernozhukov, V., I. Fernandez-Val, and A. Galichon, (2009) Improving Estimates of
Monotone Functions by Rearrangement, Biometrika, 96, 559–575.
Hardy, G.H., J.E. Littlewood, and G. Polya (1934) Inequalities, Cambridge U. Press.