# Point and Interval Rearrangement 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. package ## 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 ## 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 ```r ##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) ```

Rearrangement-package