rearrange: Rearrangement

In quantreg: Quantile Regression

Rearrangement

Description

Monotonize a step function by rearrangement

Usage

 rearrange(f,xmin,xmax) 

Arguments

f	object of class stepfun
xmin	minimum of the support of the rearranged f
xmax	maximum of the support of the rearranged f

Details

Given a stepfunction Q(u), not necessarily monotone, let F(y) = \int \{ Q(u) \le 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) \ge 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.

See Also

rq rearrange

Examples

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"))

quantreg documentation built on Oct. 22, 2024, 5:07 p.m.