

   JJaacckkkknniiffee EEssttiimmaattiioonn

        jackknife(x, theta, ...)

   AArrgguummeennttss::

          x: a vector containing the data. To jackknife  more
             complex data structures (e.g. bivariate data) see
             the last example below.

      theta: function to be jackknifed. Takes `x' as an argu-
             ment, and may take additional arguments (see below
             and last example).

        ...: any additional arguments to be passed to `theta'

   VVaalluuee::

        list with the following components

    jack.se: The jackknife estimate of standard error of
             `theta'.  The leave-one out jackknife is used.

   jack.bias: The jackknife estimate of bias of `theta'.  The
             leave-one out jackknife is used.

   jack.values: The n leave-one-out values of `theta', where n
             is the number of observations.  That is, `theta'
             applied to `x' with the 1st observation deleted,
             `theta' applied to `x' with the 2nd observation
             deleted, etc.

   RReeffeerreenncceess::

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

   EExxaammpplleess::

        # jackknife values for the sample mean
        # (this is for illustration;  # since "mean" is  a
        #  built in function,  jackknife(x,mean) would be simpler!)
        x <- rnorm(20)
        theta <- function(x){mean(x)}

        results <- jackknife(x,theta)

        # To jackknife 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 jackknife the vector 1,2,..n.
        # For example, to jackknife
        # 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 <- jackknife(1:n,theta,xdata)

