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Calculate percentile bootstrap confidence interval

Source: R/perc_ci.R
perc_ci.Rd

This function calculates a percentile confidence interval from a bootstrap sample. It is used by calculate_bootstrap_ci().

Usage

perc_ci(t, conf = 0.95, h = function(t) t, hinv = function(t) t)

Arguments

t

Numeric vector of bootstrap replicates.

conf

A numeric value specifying the confidence level of the interval. Default is 0.95 (95 % confidence level).

h

A function defining a transformation. The intervals are calculated on the scale of h(t) and the inverse function hinv applied to the resulting intervals. It must be a function of one variable only. The default is the identity function.

hinv

A function, like h, which returns the inverse of h. It is used to transform the intervals calculated on the scale of h(t) back to the original scale. The default is the identity function. If h is supplied but hinv is not, then the intervals returned will be on the transformed scale.

Value

A matrix with four columns:

  • conf: confidence level

  • rk_lower: rank of lower endpoint (interpolated)

  • rk_upper: rank of upper endpoint (interpolated)

  • ll: lower confidence limit

  • ul: lower confidence limit

Details

$$CI_{perc} = \left[ \hat{\theta}^*_{(\alpha/2)}, \hat{\theta}^*_{(1-\alpha/2)} \right]$$

where \(\hat{\theta}^*_{(\alpha/2)}\) and \(\hat{\theta}^*_{(1-\alpha/2)}\) are the \(\alpha/2\) and \(1-\alpha/2\) percentiles of the bootstrap distribution, respectively.

Note

This function is adapted from the internal function perc.ci() in the boot package (Canty & Ripley, 1999).

References

Canty, A., & Ripley, B. (1999). boot: Bootstrap Functions (Originally by Angelo Canty for S) [Computer software]. https://CRAN.R-project.org/package=boot

Davison, A. C., & Hinkley, D. V. (1997). Bootstrap Methods and their Application (1st ed.). Cambridge University Press. doi:10.1017/CBO9780511802843

See also

Other interval_calculation: basic_ci(), bca_ci(), norm_ci()

Examples

set.seed(123)
boot_reps <- rnorm(1000)      # bootstrap replicates
t0 <- mean(boot_reps)         # observed statistic

# Percentile CI
perc_ci(boot_reps, conf = 0.95)
#>      conf rk_lower rk_upper       ll       ul
#> [1,] 0.95    25.03   975.98 -1.94292 2.049767