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.

See also

bootstrap()

Other summary statistics: confidence_binomial(), confidence_mean(), confidence_multinomial(), interval_credible(), interval_hdr()

Author

N. Frerebeau

Examples

x <- rnorm(20)

## Bootstrap
bootstrap(x, do = mean, n = 100)
#>    original        mean        bias       error       lower       upper 
#>  0.08847361  0.11258922  0.02411562  0.21393003 -0.34954034  0.42490420 

## 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% 
#> -0.03671968  0.19907598 

## Get the n bootstrap estimates
(z <- bootstrap(x, n = 100, do = mean, f = function(x) { x }))
#>   [1]  0.299590840  0.320153362 -0.259288473  0.164339635 -0.191425231
#>   [6] -0.139810495  0.007416607  0.605360140 -0.166575424 -0.101487988
#>  [11]  0.284748786 -0.007499523  0.004304247  0.218994186  0.021125206
#>  [16] -0.056810271  0.059417104  0.161721338  0.015272930  0.375422699
#>  [21] -0.181868435 -0.073487916  0.481650836  0.010074723  0.071206967
#>  [26]  0.372160851  0.036152294 -0.067253393  0.093160454  0.034911981
#>  [31] -0.137134500 -0.036490132  0.138077415 -0.006572719 -0.093006522
#>  [36] -0.107602651  0.135752342  0.347914464  0.104548394  0.444301665
#>  [41] -0.242253547  0.129326933 -0.366982591 -0.123817158  0.039819078
#>  [46] -0.219225440  0.216401111 -0.185099896  0.286339982  0.364277313
#>  [51] -0.151321700 -0.130989564 -0.320399508  0.164000414  0.304848028
#>  [56]  0.066714927  0.287280325  0.404297289 -0.135315156  0.274131629
#>  [61] -0.023868809 -0.043658558 -0.188440347  0.121464000  0.427792841
#>  [66] -0.244275523  0.338741256  0.050022740  0.125660580  0.191986260
#>  [71] -0.027042996  0.046467118 -0.025826127  0.208498186  0.057714806
#>  [76]  0.024286810 -0.298886092  0.105710051 -0.087564438  0.422712513
#>  [81]  0.028811940  0.385162438  0.009321958  0.073221907 -0.172764748
#>  [86]  0.283707623  0.300469991  0.184487593  0.059698065  0.100689400
#>  [91]  0.224082588 -0.077634668  0.490145448  0.045453867  0.113023531
#>  [96]  0.078186624  0.235919571  0.625720208  0.046847795  0.232525693

## Basic bootstrap confidence interval
confidence_bootstrap(z, level = 0.95, type = "basic", t0 = mean(x))
#>      lower      upper 
#> -0.3630975  0.4851507