bootstrap {bootstrap} | R Documentation |

## Non-Parametric Bootstrapping

### Description

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

### Usage

```
bootstrap(x,nboot,theta,..., func=NULL)
```

### Arguments

`x` |
a vector containing the data. To bootstrap more complex data structures (e.g. bivariate data) see the last example below. |

`nboot` |
The number of bootstrap samples desired. |

`theta` |
function to be bootstrapped. Takes |

`...` |
any additional arguments to be passed to |

`func` |
(optional) argument specifying the functional the distribution of thetahat that is desired. If func is specified, the jackknife after-bootstrap estimate of its standard error is also returned. See example below. |

### Value

list with the following components:

`thetastar` |
the |

`func.thetastar` |
the functional |

`jack.boot.val` |
the jackknife-after-bootstrap values for |

`jack.boot.se` |
the jackknife-after-bootstrap standard error
estimate of |

`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. (1992) Jackknife-after-bootstrap standard errors and influence functions. J. Roy. Stat. Soc. B, vol 54, pages 83-127

Efron, B. and Tibshirani, R. (1993) An Introduction to the Bootstrap. Chapman and Hall, New York, London.

### Examples

```
# 100 bootstraps of the sample mean
# (this is for illustration; since "mean" is a
# built in function, bootstrap(x,100,mean) would be simpler!)
x <- rnorm(20)
theta <- function(x){mean(x)}
results <- bootstrap(x,100,theta)
# as above, but also estimate the 95th percentile
# of the bootstrap dist'n of the mean, and
# its jackknife-after-bootstrap standard error
perc95 <- function(x){quantile(x, .95)}
results <- bootstrap(x,100,theta, func=perc95)
# To bootstrap 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 bootstrap the vector 1,2,..n.
# For example, to bootstrap
# 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 <- bootstrap(1:n,20,theta,xdata)
```

*bootstrap*version 2019.6 Index]