# 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

 ```1 2``` ```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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ```# 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) ```

bootstrap documentation built on May 29, 2017, 8:37 p.m.