Nonparametric ABC Confidence Limits
See Efron and Tibshirani (1993) for details on this function.
abcnon(x, tt, epsilon=0.001, alpha=c(0.025, 0.05, 0.1, 0.16, 0.84, 0.9, 0.95, 0.975))
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
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
call: The deparsed call
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.
# 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[, 1] - x1m)^2) * sum(p * (x[, 2] - x2m)^2)) return(num/den) } results <- abcnon(x, theta)