# jackknife: Jackknife Estimation In bootstrap: Functions for the Book "An Introduction to the Bootstrap"

## Description

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

## Usage

 `1` ``` 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```# 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) ```

### Example output

```
```

bootstrap documentation built on June 17, 2019, 5:04 p.m.