boot (version 1.2-10)

abc.ci: Nonparametric ABC Confidence Intervals

Description

Calculate equi-tailed two-sided nonparametric approximate bootstrap confidence intervals for a parameter, given a set of data and an estimator of the parameter, using numerical differentiation.

Usage

abc.ci(data, statistic, index=1, strata=rep(1, n), conf=0.95, 
       eps=0.001/n, ...)

Arguments

data

A data set expressed as a vector, matrix or data frame.

statistic

A function which returns the statistic of interest. The function must take at least 2 arguments; the first argument should be the data and the second a vector of weights. The weights passed to statistic will be normalized to sum to 1 withi

Value

• A length(conf) by 3 matrix where each row contains the confidence level followed by the lower and upper end-points of the ABC interval at that level.

item

• index
• strata
• conf
• eps
• ...

code

abc.ci

Details

This function is based on the function abcnon written by R. Tibshirani. A listing of the original function is available in DiCiccio and Efron (1996). The function uses numerical differentiation for the first and second derivatives of the statistic and then uses these values to approximate the bootstrap BCa intervals. The total number of evaluations of the statistic is 2*n+2+2*length(conf) where n is the number of data points (plus calculation of the original value of the statistic). The function works for the multiple sample case without the need to rewrite the statistic in an artificial form since the stratified normalization is done internally by the function.

References

Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application, Chapter 5. Cambridge University Press.

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

DiCiccio, T. J. and Efron B. (1996) Bootstrap confidence intervals (with Discussion). Statistical Science, 11, 189--228.

See Also

boot.ci

Examples

# 90\% and 95\% confidence intervals for the correlation 
# coefficient between the columns of the bigcity data


data(bigcity)
abc.ci(bigcity, corr, conf=c(0.90,0.95))


data(gravity)
# A 95\% confidence interval for the difference between the means of
# the last two samples in gravity
mean.diff <- function(y, w)
{    gp1 <- 1:table(as.numeric(y$series))[1]
     sum(y[gp1,1] * w[gp1]) - sum(y[-gp1,1] * w[-gp1])
}
grav1 <- gravity[as.numeric(gravity[,2])>=7,]
abc.ci(grav1, mean.diff, strata=grav1$series)