R: Non-Parametric Bootstrapping

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 `x` as an argument, and may take additional arguments (see below and last example).
`...` | any additional arguments to be passed to `theta`
`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 `nboot` bootstrap values of `theta`
`func.thetastar` | the functional `func` of the bootstrap distribution of thetastar, if `func` was specified
`jack.boot.val` | the jackknife-after-bootstrap values for `func`, if `func` was specified
`jack.boot.se` | the jackknife-after-bootstrap standard error estimate of `func`, if `func` was specified
`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)

[Package bootstrap version 2019.6 Index]