Non-parametric bootstrapping

USAGE:
       bootstrap(x,nboot,theta,..., func=NULL)

ARGUMENTS:
x:     a vector containing the data. To bootstrap   more  complex
       data  structures (e.g bivariate data) see the last example
       below.
nboot:    The number of bootstrap samples desired.
theta:    function to be bootstrapped. Takes x  as  an  argument,
       and  may  take  additional  arguments  (see below and last
       example).
...:   any additional arguments to be passed to theta
func:      (optional)  argument  specifying  the  functional  the
       distribution  of  thetahat  that  is  desired.  If func is
       specified, the jackknife after-bootstrap estimate  of  its
       standard error is also returned. See example below.





VALUE:
       list with the following components:

thetastar:      the nboot bootstrap values of theta

func.thetastar:        the  functional  func  of  the   bootstrap
       distribution of thetastar, if func was specified

jack.boot.val:   the jackknife-after-bootstrap values  for  func,
       if func was specified

jack.boot.se:     the  jackknife-after-bootstrap  standard  error
       estimate of func, if func was specified



REFERENCES:
         Efron, B. and   Tibshirani, R. (1986).  The bootstrap
        method for standard  errors,  confidence  intervals,  and
       other measures of   statistical accuracy.
         Statistical Science, Vol 1., No. 1, pp 1-35.

       Efron, B. (1992) Jackknife-after-bootstrap standard errors
       and  influence  functions.   J. Roy. Stat. Soc. B, vol 54,
       pages 83-127

       Efron, B. and Tibshirani, R. (1993) An Introduction to the
       Bootstrap.  Chapman and Hall, New York, London.



EXAMPLES:

       # 100 bootstraps of the sample mean
       # (this is for illustration;  since "mean" is  a
       # built in function, bootstrap(x,100,mean) would be simpler!)

       x <- rnorm(20)
       theta <- function(x){mean(x)}

       results <- bootstrap(x,100,theta)

       # as above, but also estimate the 95th percentile
       # of the bootstrap dist'n of the mean, and
       # its jackknife-after-bootstrap  standard error

       perc95 <- function(x){quantile(x, .95)}


       results <-  bootstrap(x,100,theta, func=perc95)





       # To bootstrap functions of more complex data structures,
       # write theta so that its argument x
       #  is the set of observation numbers
       #  and simply  pass as data to bootstrap the vector 1,2,..n.
       # For example, to bootstrap
       # the correlation coefficient from a set of 15 data pairs:

       xdata <- matrix(rnorm(30),ncol=2)
       n <- 15
       theta <- function(x,xdata){ cor(xdata[x,1],xdata[x,2]) }
       results <- bootstrap(1:n,20,theta,xdata)