Rearrangement-package {Rearrangement}

Point and Interval Rearrangement

Description

This package implements the rearrangement operator (Hardy, Littlewood, and Polya 1952) for univariate, bivariate, and trivariate point estimates of monotonic functions. It additionally provides a function that creates simultaneous confidence intervals for univariate functions and applies the rearrangement operator to these confidence intervals.

Details

Package:	Rearrangement
Type:	Package
Version:	1.0
Date:	2011-09-11
License:	GPL(>=2)
LazyLoad:	yes

This package is used for rearranging both point and interval estimates of a target function. Given an original point estimate of a target function, one may use rearrangement to monotonize this estimate. One may also create simultaneous confidence interval estimates using simconboot and monotonize these estimates using rconint.

Author(s)

Wesley Graybill, Mingli Chen, Victor Chernozhukov, Ivan Fernandez-Val, Alfred Galichon

Maintainer: Ivan Fernandez-Val <[e-mail]>

References

Chernozhukov, V., I. Fernandez-Val, and a. Galichon. 2009. Improving point and interval estimators of monotone functions by rearrangement. Biometrika 96 (3): 559-575.

Chernozhukov, V., I. Fernandez-Val, and a. Galichon. 2010. Quantile and Probability Curves Without Crossing. Econometrica 78(3): 1093-1125.

Hardy, G.H., J.E. Littlewood, and G. Polya, Inequalities,2nd ed, Cambridge U. Press,1952

Examples

##rearrangement example:
library(splines)
data(GrowthChart)
attach(GrowthChart)

ages <- unique(sort(age))
aknots <- c(3, 5, 8, 10, 11.5, 13, 14.5, 16, 18)
splines_age <- bs(age,kn=aknots)
sformula <- height~splines_age
sfunc <- approxfun(age,lm(sformula)$fitted.values)
splreg <- sfunc(ages)
rsplreg <- rearrangement(list(ages),splreg)
plot(age,height,pch=21,bg='gray',cex=.5,xlab="Age(years)",
ylab="Height(cms)", main="CEF (Regression Splines)",col='gray')
lines(ages,splreg,col='red',lwd=3)
lines(ages,rsplreg,col='blue',lwd=2)
legend("topleft",c('Original','Rearranged'),lty=1,col=c('red','blue'),bty='n')
detach(GrowthChart)

##rconint example:
## Not run: 
data(GrowthChart)
attach(GrowthChart)

nage <- 2 * pi * (age - min(age)) / (max(age) - min(age))

formula <- height~I(sin(nage))+I(cos(nage))+I(sin(2*nage)) +
            I(cos(2*nage))+I(sin(3*nage))+
            I(cos(3*nage))+ I(sin(4*nage)) + I(cos(4*nage))
			
j <- simconboot(nage,height,lm,formula)
k <- rconint(j)
plot(k, border=NA, col='darkgray')
polygon.conint(j, border=NA, col='lightgray')
polygon.conint(k, border=NA, col='darkgray', density=50)
points(nage,height)
detach(GrowthChart)

## End(Not run)