abc.ci {boot}  R Documentation 
Calculate equitailed twosided nonparametric approximate bootstrap confidence intervals for a parameter, given a set of data and an estimator of the parameter, using numerical differentiation.
abc.ci(data, statistic, index=1, strata=rep(1, n), conf=0.95, eps=0.001/n, ...)
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 within each stratum. Any other arguments should be
passed to abc.ci as part of the ...{} argument.

index 
If statistic returns a vector of length greater than 1, then this indicates
the position of the variable of interest within that vector.

strata 
A factor or numerical vector indicating to which sample each observation belongs in multiple sample problems. The default is the onesample case. 
conf 
A scalar or vector containing the confidence level(s) of the required interval(s). 
eps 
The value of epsilon to be used for the numerical differentiation. 
... 
Any other arguments for statistic . These will be passed unchanged to
statistic each time it is called within abc.ci .

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.
A length(conf)
by 3 matrix where each row contains the confidence level
followed by the lower and upper endpoints of the ABC interval at that
level.
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.
# 90% and 95% confidence intervals for the correlation # coefficient between the columns of the bigcity data abc.ci(bigcity, corr, conf=c(0.90,0.95)) # 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)