Rearrangement
Monotonize a step function by rearrangement
rearrange(f,xmin,xmax)
f |
object of class stepfun |
xmin |
minimum of the support of the rearranged f |
xmax |
maximum of the support of the rearranged f |
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.
Produces transformed stepfunction that is monotonic increasing.
R. Koenker
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.
data(engel)
z <- rq(foodexp ~ income, tau = -1,data =engel)
zp <- predict(z,newdata=list(income=quantile(engel$income,.03)),stepfun = TRUE)
plot(zp,do.points = FALSE, xlab = expression(tau),
ylab = expression(Q ( tau )), main="Engel Food Expenditure Quantiles")
plot(rearrange(zp),do.points = FALSE, add=TRUE,col.h="red",col.v="red")
legend(.6,300,c("Before Rearrangement","After Rearrangement"),lty=1,col=c("black","red"))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.