TITLE(abcpar @@ Parametric  ABC  confidence limits  )
USAGE(
abcpar(x, tt, S, etahat, mu, n=rep(1,length(x)),lambda=0.001, 
 alpha=c(0.025, 0.05, 0.1, 0.16))
)
ARGUMENTS(
ARG(x@@vector of data)
ARG(tt@@
function of expectation parameter mu defining the parameter of interest)
ARG(S@@
maximum likelihood estimate of the  covariance matrix of x)
ARG(etahat@@
maximum likelihood estimate of the natural parameter eta)
ARG(mu@@
function giving expectation of x in terms of eta)
ARG(n@@
optional argument containing denominators for binomial (vector of
length length(x))) 
ARG(lambda@@
optional argument specifying step size for finite difference calculation)
ARG(alpha@@
optional argument specifying confidence levels desired)
)
VALUES(
list with the following components
ARG(call@@
the call to abcpar)
ARG(limits@@
The nominal confidence level, ABC point, quadratic ABC point, and
standard normal point.) 
ARG(stats@@
list consisting of  observed value of tt, estimated standard error and estimated bias)
ARG(constants@@
list consisting of a=acceleration constant, z0=bias adjustment,
cq=curvature component)
)
REFERENCES(
Efron, B, and DiCiccio, T. (1992) More accurate confidence intervals 
in exponential families. Bimometrika 79, pages 231-245.
PARA
Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap.
Chapman and Hall, New York, London.
)
EXAMPLES(
# binomial
# x is a p-vector of successes, n is a p-vector of 
#  number of trials
S <- matrix(0,nrow=p,ncol=p)
S[row(S)==col(S)] <- x*(1-x/n)
mu <- function(eta,n)\{n/(1+exp(eta))\}
etahat <- log(x/(n-x))
#suppose p=2 and we are interested in mu2-mu1
tt <- function(mu)\{mu[2]-mu[1]\}
x <- c(2,4); n <- c(12,12)
a <- abcpar(x, tt, S, etahat,n)
)

