jackknife {bootstrap}

Jackknife Estimation

Description

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

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.

call

The deparsed call

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)