TITLE(abcnon @@ Nonparametric ABC confidence limits)
USAGE(
abcnon(x, tt, epsilon=0.001, 
 alpha=c(0.025, 0.05, 0.1, 0.16, 0.84, 0.9, 0.95, 0.975))
)
ARGUMENTS(
ARG(x @@ the data. Must be either a vector, or a matrix whose rows are
the observations)
ARG(tt @@ function defining the parameter in the resampling form
tt(p,x), where p is the vector of proportions and x is the data)
ARG(epsilon @@ optional argument specifying step size for finite
difference calculations) 
ARG(alpha @@ optional argument specifying confidence levels desired)
)
VALUES(
list with following components
ARG(limits @@ 
The estimated confidence points, from the ABC and standard normal methods)
ARG(stats @@ 
list consisting of t0=observed value of tt, sighat=infinitesimal jackknife estimate
 of standard error of tt, bhat= estimated bias)
ARG(constants @@
list consisting of a=acceleration constant, z0=bias adjustment,
cq=curvature component) 
ARG(tt.inf @@
approximate influence components of tt)
ARG(pp @@
matrix whose rows are the resampling points in the least favourable family .
The abc confidence points are the function tt evaluated at these
points)
)
REFERENCES(
Efron, B, and DiCiccio, T. (1992) More accurate confidence intervals 
in exponential families. Biometrika 79, pages 231-245.
PARA
Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap.
Chapman and Hall, New York, London.
)
EXAMPLES(
# compute abc intervals for the mean
x <- rnorm(10)
theta <- function(p,x) \{sum(p*x)/sum(p)\}
results <- abcnon(x, theta)  
# compute abc intervals for the correlation
x <- matrix(rnorm(20),ncol=2)
theta <- function(p, x)
\{
    x1m <- sum(p * x[, 1])/sum(p)
    x2m <- sum(p * x[, 2])/sum(p)
    num <- sum(p * (x[, 1] - x1m) * (x[, 2] - x2m))
    den <- sqrt(sum(p * (x[, 2] - x1m)^2) *
              sum(p * (x[, 2] - x1m)^2))
    return(num/den)
\}
results <- abcnon(x, theta)   
)