

   NNoonnppaarraammeettrriicc BBCCaa CCoonnffiiddeennccee LLiimmiittss

        bcanon(x, nboot, theta, ...,
               alpha=c(0.025, 0.05, 0.1, 0.16, 0.84, 0.9, 0.95, 0.975))

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

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

      nboot: number of bootstrap replications

      theta: function defining the estimator used in construct-
             ing the confidence points

        ...: additional arguments for `theta'

      alpha: optional argument specifying confidence levels
             desired

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

        list with the following components

   confpoint: estimated bca confidence limits

         z0: estimated bias correction

        acc: estimated acceleration constant

          u: jackknife influence values

   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. (1987). Better bootstrap confidence intervals
        (with discussion).  J. Amer. Stat. Assoc. vol 82, pg
        171

        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::

        #  bca limits for the  mean
        #  (this is for illustration;
        #   since "mean" is a built in function,
        #   bcanon(x,100,mean) would be simpler!)
        x <- rnorm(20)
        theta <- function(x){mean(x)}
        results <- bcanon(x,100,theta)

        # To obtain bca limits for 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 bcanon
        # the vector 1,2,..n.
        # For example, find bca limits for
        # 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 <- bcanon(1:n,100,theta,xdata)

