bootstrap (version 2014.4)

abcnon: Nonparametric ABC Confidence Limits

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)