# bootci.r                 December 2007
 #
 # bootstrap confidence interval
 #
 #
 # set up
 #
 #  Exercise 8.13 -- least 3/2's estimator
 #
 #  define function
  g3o2 <- function(x) {
 #                  derivative of function to be minimized
    fp3o2 <- function (mu,u) { # derivative  
            fp3o2 <- sum( sign(u-mu)*sqrt(abs(u-mu)) ) }
 #  
 #  find root of derivative function
    that2 <- uniroot(f=fp3o2, lower=min(x), upper=max(x), u=x )
    g3o2 <- that2$root        }    # root is statistic
 #
 #  data
  v <- c(225,215,209,175,163,135,153,125)
 #
  print(g3o2(v))        # compute statistic on data
 # First method -- create matrix and use apply
 # data
  set.seed(5151917)
  Nboot <- 999          # DB suggests 99 rule
  g3o2(v)               # compute statistic on data
 # 
 #
 #       sample from v -- how many? length(v)*Nboot, WITH replacement
 #     matrix  so that each column is a bootstrap sample
  V <- matrix(sample(v,length(v)*Nboot,replace=T),length(v),Nboot)
 # compute statistic
  vstar <- apply(V,2,g3o2)
 # simple statistics
  var(vstar)
  mean(vstar)
 # order statistics give CI limits
  vStar <- sort(vstar)
 #  first 90% confidence interval
  c(vStar[49],vStar[950])
 #  then  95%
  c(vStar[24],vStar[975])
 #
 # done
  rm(list=ls())
 q()