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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
x
|
vector of data
|
tt
|
function of expectation parameter mu defining the parameter of interest
|
S
|
maximum likelihood estimate of the covariance matrix of x
|
etahat
|
maximum likelihood estimate of the natural parameter eta
|
mu
|
function giving expectation of x in terms of eta
|
n
|
optional argument containing denominators for binomial (vector of
length length(x) )
|
lambda
|
optional argument specifying step size for finite difference calculation
|
alpha
|
optional argument specifying confidence levels desired
|
Value
list with the following components
call
|
the call to abcpar
|
limits
|
The nominal confidence level, ABC point, quadratic ABC point, and
standard normal point.
|
stats
|
list consisting of observed value of tt , estimated standard error and estimated bias
|
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.
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)