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Jackknife Estimation
Usage
jackknife(x, theta, ...)
Arguments
x
|
a vector containing the data. To jackknife more complex data
structures (e.g. bivariate data) see the last example below.
|
theta
|
function to be jackknifed. Takes x as an argument, and
may take additional arguments (see below and last example).
|
...
|
any additional arguments to be passed to theta
|
Value
list with the following components
jack.se
|
The jackknife estimate of standard error of theta .
The leave-one out jackknife is used.
|
jack.bias
|
The jackknife estimate of bias of theta .
The leave-one out jackknife is used.
|
jack.values
|
The n leave-one-out values of theta ,
where n is the number of observations.
That is, theta applied to x with
the 1st observation deleted, theta applied to x with
the 2nd observation deleted, etc.
|
References
Efron, B. and Tibshirani, R. (1986). The Bootstrap
Method for standard errors, confidence intervals,
and other measures of statistical accuracy.
Statistical Science, Vol 1., No. 1, pp 1-35.
Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap.
Chapman and Hall, New York, London.
Examples
# jackknife values for the sample mean
# (this is for illustration; # since "mean" is a
# built in function, jackknife(x,mean) would be simpler!)
x <- rnorm(20)
theta <- function(x){mean(x)}
results <- jackknife(x,theta)
# To jackknife functions of more complex data structures,
# write theta so that its argument x
# is the set of observation numbers
# and simply pass as data to jackknife the vector 1,2,..n.
# For example, to jackknife
# the correlation coefficient from a set of 15 data pairs:
xdata <- matrix(rnorm(30),ncol=2)
n <- 15
theta <- function(x,xdata){ cor(xdata[x,1],xdata[x,2]) }
results <- jackknife(1:n,theta,xdata)