abcpar {bootstrap}

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)