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]