abcnon function

Nonparametric ABC Confidence Limits

Nonparametric ABC Confidence Limits

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

abcnon(x, tt, epsilon=0.001, alpha=c(0.025, 0.05, 0.1, 0.16, 0.84, 0.9, 0.95, 0.975))

Arguments

  • x: the data. Must be either a vector, or a matrix whose rows are the observations

  • tt: function defining the parameter in the resampling form tt(p,x), where p is the vector of proportions and x

    is the data

  • epsilon: optional argument specifying step size for finite difference calculations

  • alpha: optional argument specifying confidence levels desired

Returns

list with following components - limits: The estimated confidence points, from the ABC and standard normal methods

  • stats: list consisting of t0=observed value of tt, sighat=infinitesimal jackknife estimate of standard error of tt, bhat=estimated bias

  • constants: list consisting of a=acceleration constant, z0=bias adjustment, cq=curvature component

  • tt.inf: approximate influence components of tt

  • pp: matrix whose rows are the resampling points in the least favourable family. The abc confidence points are the function tt

    evaluated at these points

  • call: The deparsed call

References

Efron, B, and DiCiccio, T. (1992) More accurate confidence intervals in exponential families. Biometrika 79, pages 231-245.

Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London.

Examples

# compute abc intervals for the mean x <- rnorm(10) theta <- function(p,x) {sum(p*x)/sum(p)} results <- abcnon(x, theta) # compute abc intervals for the correlation x <- matrix(rnorm(20),ncol=2) theta <- function(p, x) { x1m <- sum(p * x[, 1])/sum(p) x2m <- sum(p * x[, 2])/sum(p) num <- sum(p * (x[, 1] - x1m) * (x[, 2] - x2m)) den <- sqrt(sum(p * (x[, 1] - x1m)^2) * sum(p * (x[, 2] - x2m)^2)) return(num/den) } results <- abcnon(x, theta)
  • Maintainer: Scott Kostyshak
  • License: BSD_3_clause + file LICENSE
  • Last published: 2019-06-17