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
x
|
the data. Must be either a vector, or a matrix whose rows are
the observations
|
tt
|
function defining the parameter in the resampling form
tt(p,x) , where p is the vector of proportions and x
is the data
|
epsilon
|
optional argument specifying step size for finite
difference calculations
|
alpha
|
optional argument specifying confidence levels desired
|
Value
list with following components
limits
|
The estimated confidence points, from the ABC and standard normal methods
|
stats
|
list consisting of t0 =observed value of tt ,
sighat =infinitesimal jackknife estimate
of standard error of tt , bhat =estimated bias
|
constants
|
list consisting of a =acceleration constant,
z0 =bias adjustment, cq =curvature component
|
tt.inf
|
approximate influence components of tt
|
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.
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)