R: Rearrangement

rearrange {quantreg} | R Documentation

## 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) ≤ 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.

### 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"))

[Package quantreg version 5.83 Index]