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]