abcpar function

Parametric ABC Confidence Limits

Parametric ABC Confidence Limits

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

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

Returns

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)
  • Maintainer: Scott Kostyshak
  • License: BSD_3_clause + file LICENSE
  • Last published: 2019-06-17