Nonparametric Bootstrap Confidence Interval

Computes equi-tailed two-sided nonparametric confidence interval.

Usage

confidence_bootstrap(object, ...)

# S4 method for class 'numeric'
confidence_bootstrap(
  object,
  level = 0.95,
  type = c("basic", "normal", "student", "percentiles"),
  t0 = NULL,
  var_t0 = NULL,
  var_t = NULL,
  ...
)

Arguments

object: A numeric vector giving the bootstrap replicates of the statistic of interest.
...: Currently not used.
level: A length-one numeric vector giving the confidence level. Must be a single number between \(0\) and \(1\).
type: A character string giving the type of confidence interval to be returned. It must be one "basic" (the default), "student", "normal" or "percentiles". Any unambiguous substring can be given.
t0: A length-one numeric vector giving the observed value of the statistic of interest. Must be defined if type is "basic", "student" or "normal".
var_t0: A length-one numeric vector giving an estimate of the variance of the statistic of interest. Must be defined if type is "student". If var_t0 is undefined and type is "normal, it defaults to var(object).
var_t: A numeric vector giving the variances of the bootstrap replicates of the variable of interest. Must be defined if type is "student".

Value

A length-two numeric vector giving the lower and upper confidence limits.

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 
#>  0.08279935  0.09685068  0.01405133  0.20377014 -0.26938036  0.47008738 

## 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% 
#> -0.09889091  0.22972109 

## Get the n bootstrap estimates
(z <- bootstrap(x, n = 100, do = mean, f = function(x) { x }))
#>   [1] -0.035656778 -0.053098012  0.014194773 -0.304153085  0.429528200
#>   [6]  0.309721402 -0.301880008 -0.494729833  0.170585485  0.368156817
#>  [11] -0.008692328 -0.309785421 -0.430884902  0.038125908  0.150895816
#>  [16]  0.063440799  0.403047158 -0.254249105  0.277451781 -0.180174048
#>  [21]  0.136977561  0.133339186 -0.219018859  0.001371939  0.151657349
#>  [26]  0.076535065 -0.015714782  0.054881079  0.270960997  0.420687834
#>  [31] -0.026064502  0.451707491  0.149567475 -0.038791862  0.042045703
#>  [36] -0.253326216  0.294054191 -0.278628210  0.247845605  0.408845224
#>  [41]  0.252016122 -0.172545540  0.147479587  0.070363716  0.204599572
#>  [46]  0.069778831  0.340138888  0.363690882  0.446092193  0.190168714
#>  [51]  0.080816400 -0.140582569  0.104200511 -0.057835514  0.192533291
#>  [56]  0.452635100 -0.127770213  0.119903582 -0.042454819  0.320664719
#>  [61]  0.221692723  0.012401290  0.300825087 -0.076051473 -0.029352389
#>  [66]  0.042625162  0.342830883  0.437672541  0.182484926 -0.045915373
#>  [71]  0.289773492 -0.122575438  0.014241826 -0.171322535  0.359392484
#>  [76]  0.220794210 -0.070381035  0.248234484  0.024892025 -0.045864214
#>  [81]  0.113510789  0.365889324  0.083406503  0.020579296 -0.026991366
#>  [86]  0.268508480  0.366075776  0.048669628  0.414410266 -0.287654397
#>  [91] -0.026251097  0.114271864  0.486579786  0.079339214  0.174145719
#>  [96]  0.049649180 -0.194323305  0.206408981 -0.060836371  0.104003501

## Basic bootstrap confidence interval
confidence_bootstrap(z, level = 0.95, type = "basic", t0 = mean(x))
#>      lower      upper 
#> -0.2865105  0.5278321