R: Parametric ABC Confidence Limits

abcpar {bootstrap} | R Documentation

## Parametric ABC Confidence Limits

### Description

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

### Usage

    abcpar(y, tt, S, etahat, mu, n=rep(1,length(y)),lambda=0.001,
           alpha=c(0.025, 0.05, 0.1, 0.16))

### Arguments

`y` | vector of data
`tt` | function of expectation parameter `mu` defining the parameter of interest
`S` | maximum likelihood estimate of the covariance matrix of `x`
`etahat` | maximum likelihood estimate of the natural parameter eta
`mu` | function giving expectation of `x` in terms of eta
`n` | optional argument containing denominators for binomial (vector of length `length(x)`)
`lambda` | optional argument specifying step size for finite difference calculation
`alpha` | optional argument specifying confidence levels desired

### Value

list with the following components

`call` | the call to abcpar
`limits` | The nominal confidence level, ABC point, quadratic ABC point, and standard normal point.
`stats` | list consisting of observed value of `tt`, estimated standard error and estimated bias
`constants` | list consisting of `a`=acceleration constant, `z0`=bias adjustment, `cq`=curvature component

,

`asym.05` | asymmetry component

### References

Efron, B, and DiCiccio, T. (1992) More accurate confidence intervals in exponential families. Bimometrika 79, pages 231-245.

Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London.

### Examples

    # binomial
    # x is a p-vector of successes, n is a p-vector of
    #  number of trials
    ## Not run:
    S <- matrix(0,nrow=p,ncol=p)
    S[row(S)==col(S)] <- x*(1-x/n)
    mu <- function(eta,n){n/(1+exp(eta))}
    etahat <- log(x/(n-x))
    #suppose p=2 and we are interested in mu2-mu1
    tt <- function(mu){mu[2]-mu[1]}
    x <- c(2,4); n <- c(12,12)
    a <- abcpar(x, tt, S, etahat,n)

    ## End(Not run)

[Package bootstrap version 2019.6 Index]