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 
#> -0.31003022 -0.36538846 -0.05535824  0.25116541 -0.80452446  0.29147031 

## 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% 
#> -0.4233110 -0.1714454 

## Get the n bootstrap estimates
(z <- bootstrap(x, n = 100, do = mean, f = function(x) { x }))
#>   [1]  0.05882350 -0.15970975 -0.16824740 -0.25337802  0.38357259 -0.27767305
#>   [7] -0.56937703 -0.17413748 -0.52393747 -0.03761762 -0.37639113 -0.62335220
#>  [13]  0.02098242 -0.48991571 -0.38256150 -0.35694976 -0.07544047 -0.28480161
#>  [19] -0.38464752 -0.55362749 -0.27333930 -0.48971194 -0.11691814 -0.98175087
#>  [25] -0.74759480 -0.38207080 -0.52612229 -0.52627593 -0.48806821 -0.03992511
#>  [31] -0.38862562 -0.01227077 -0.97275850 -0.41971631 -0.03975755 -0.07345552
#>  [37] -0.47651196  0.07988537 -0.34898297 -0.52959421 -0.32875221 -0.53683465
#>  [43] -0.53870283 -0.15155093 -0.22187541 -0.55008251 -0.93603395 -0.25134170
#>  [49]  0.09068206 -0.30633353  0.01512999  0.02636154 -0.62805636 -0.41543211
#>  [55] -0.73731395 -0.60169945 -0.10066947 -0.26596719 -0.10152999  0.01594432
#>  [61] -0.20390957  0.25543398 -0.17004627 -1.00197428  0.03192212  0.09843582
#>  [67] -0.71917920 -0.72579064 -0.39998269 -0.49303580 -0.37553424 -0.42163805
#>  [73] -0.42700161 -0.26265073 -0.43257369 -0.29944782 -0.33025893 -0.21952608
#>  [79] -0.33849245 -0.68065268 -0.25271155  0.12362128  0.01747910 -0.54110655
#>  [85] -0.15135539  0.03421979 -0.06693228 -0.79303070 -0.04313817 -0.34621952
#>  [91]  0.25973890 -0.57828512 -0.18786661 -0.05036271 -0.42062992 -0.10856037
#>  [97] -0.25766274 -0.01699731 -0.19125433 -0.21562539

## Basic bootstrap confidence interval
confidence_bootstrap(z, level = 0.95, type = "basic", t0 = mean(x))
#>      lower      upper 
#> -0.8773589  0.3565926