Nonparametric Bootstrap Estimation

Samples randomly from the elements of object with replacement.

Usage

bootstrap(object, ...)

# S4 method for class 'numeric'
bootstrap(
  object,
  do,
  n,
  ...,
  f = NULL,
  level = 0.95,
  interval = c("basic", "normal", "percentiles")
)

Arguments

object: A numeric vector.
...: Extra arguments to be passed to do.
do: A function that takes object as an argument and returns a single numeric value.
n: A non-negative integer giving the number of bootstrap replications.
f: A function that takes a single numeric vector (the result of do) as argument.
level: A length-one numeric vector giving the confidence level. Must be a single number between \(0\) and \(1\). Only used if f is NULL.
interval: A character string giving the type of confidence interval to be returned. It must be one "basic" (the default), "normal" or "percentiles" (see confidence_bootstrap()). Any unambiguous substring can be given. Only used if f is NULL.

Value

If f is NULL (the default), bootstrap() returns a named numeric vector with the following elements:

original: The observed value of do applied to object.
mean: The bootstrap estimate of mean of do.
bias: The bootstrap estimate of bias of do.
error: The bootstrap estimate of standard error of do.
lower: The lower limit of the bootstrap confidence interval at level.
upper: The upper limit of the bootstrap confidence interval at level

If f is a function, bootstrap() returns the result of f applied to the n values of do.

References

Davison, A. C. & Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge Series on Statistical and Probabilistic Mathematics. Cambridge: Cambridge University Press.

Author

N. Frerebeau

Examples

x <- rnorm(20)

## Bootstrap
bootstrap(x, do = mean, n = 100)
#>     original         mean         bias        error        lower        upper 
#> -0.117435227 -0.111210028  0.006225199  0.252842043 -0.778076267  0.478596745 

## Estimate the 25th and 95th percentiles
quant <- function(x) { quantile(x, probs = c(0.25, 0.75)) }
bootstrap(x, n = 100, do = mean, f = quant)
#>         25%         75% 
#> -0.25801026  0.01351363 

## Get the n bootstrap estimates
(z <- bootstrap(x, n = 100, do = mean, f = function(x) { x }))
#>   [1]  0.137742259 -0.135825915  0.253578390 -0.193667239  0.097690902
#>   [6] -0.016839800 -0.024683298 -0.203493697 -0.806142895  0.008517408
#>  [11] -0.059298045  0.142244681 -0.379590072  0.075135128  0.151848449
#>  [16] -0.031970635 -0.085168475  0.078620322 -0.504798326  0.011415927
#>  [21] -0.167885817 -0.242929365 -0.242388296 -0.361539420 -0.230708605
#>  [26]  0.178021328  0.107216373  0.001070759 -0.052606272 -0.426226594
#>  [31]  0.177273155 -0.274776655 -0.273849236 -0.405303266 -0.291506941
#>  [36]  0.255056071 -0.032611012 -0.175293090 -0.092253192 -0.073539185
#>  [41]  0.072721475 -0.002674384 -0.251180400 -0.353639786 -0.150615342
#>  [46] -0.119554964  0.314435711  0.228705683 -0.446391574 -0.347532298
#>  [51] -0.002730341 -0.141352774 -0.042585060 -0.421963234 -0.366909001
#>  [56] -0.170561779 -0.414075273 -0.306638538  0.099981261 -0.550552778
#>  [61]  0.059179184 -0.049199117 -0.244255370 -0.369697568 -0.446213655
#>  [66] -0.180721938 -0.179295629  0.007779681  0.154170218 -0.007102601
#>  [71] -0.600761116 -0.153978766 -0.437716466 -0.078592674 -0.324618440
#>  [76] -0.201995834 -0.197402623 -0.070790269 -0.095214639 -0.016974343
#>  [81] -0.485141227  0.169879450 -0.652084269 -0.336039885  0.013642024
#>  [86] -0.003301966 -0.279581277 -0.234227825 -0.349683535 -0.185248665
#>  [91]  0.053710650 -0.401383597 -0.067829885  0.142192885  0.031837535
#>  [96]  0.048959706 -0.297017210 -0.100100164 -0.549006869  0.088012025

## Basic bootstrap confidence interval
confidence_bootstrap(z, level = 0.95, type = "basic", t0 = mean(x))
#>      lower      upper 
#> -0.4890888  0.3881186