abcpar: Parametric 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

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)

bootstrap documentation built on June 17, 2019, 5:04 p.m.