abcnon {bootstrap} R Documentation

## 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)


[Package bootstrap version 2019.6 Index]