R: Nonparametric ABC Confidence Limits

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]