bootstrap (version 2012.04-0)

abcpar: 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
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)