[Previously saved workspace restored]

>  # 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
[1] 173.3705
>  # 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)
[1] 246.5115
>   mean(vstar)
[1] 173.4847
>  # order statistics give CI limits
>   vStar <- sort(vstar)
>  #  first 90% confidence interval
>   c(vStar[49],vStar[950])
[1] 150.5425 201.9542
>  #  then  95%
>   c(vStar[24],vStar[975])
[1] 142.2312 206.6722
>  #
>  # done
>   rm(list=ls())
>  q()