>  # boottest.r                 December 2007
>  #
>  # compare speeds for bootstrap
>  #
>  #
>  # set up
>  #
>  #  Exercise 8.13 -- least 3/2's estimator
>  #
>  #  define function
>   g3o2 <- function(x) {
+  #                  define function to be minimized
+     f3o2 <- function (mu)  sum((abs(x-mu)**(3/2))) 
+  #                  derivative of function to be minimizes
+     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 <- 1000
>   g3o2(v)               # compute statistic on data
>  # 
>   proc.time()       # read clock before execution
[1] 0.94 0.12 1.05 0.00 0.00
>  #
>  #       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
>   vps <- apply(V,2,g3o2)
>   proc.time()       # read clock after execution
[1] 1.58 0.12 1.70 0.00 0.00
>   var(vps)
[1] 247.5261
>   mean(vps)
[1] 173.5202
>  #
>  # Second method -- using loop
>   lv <- length(v)
>   set.seed(5151917)                # same random numbers
>   proc.time()       # read clock before execution
[1] 1.59 0.12 1.70 0.00 0.00
>   vps <- rep(0,Nboot)              # initialize to zero
>   for(i in(1:Nboot)){              # start loop
+   vbs <- sample(v,lv,replace=T)
+   vps[i]<-g3o2(vbs)           }    # end loop
>   proc.time()       # read clock after execution
[1] 2.29 0.13 2.42 0.00 0.00
>   mean(vps)
[1] 173.5202
>   var(vps)
[1] 247.5261
>  # done
>   rm(list=ls())
>  q()