abcnon: Nonparametric ABC Confidence Limits

In bootstrap: Functions for the Book "An Introduction to the Bootstrap"

Description

See Efron and Tibshirani (1993) for details on this function.

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
call	The deparsed call

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[, 1] - x1m)^2) *
              sum(p * (x[, 2] - x2m)^2))
    return(num/den)
}
results <- abcnon(x, theta)   

Example output

bootstrap documentation built on June 17, 2019, 5:04 p.m.