R: Jackknife Estimation

jackknife {bootstrap} | R Documentation

## 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)

[Package bootstrap version 2019.6 Index]