bootstrap_CIs: Calculate one or multiple bootstrap confidence intervals

Description

Calculate one or multiple bootstrap confidence intervals, given a sample of bootstrap replications.

Usage

bootstrap_CIs(
  boot_est,
  boot_se = NULL,
  est = NULL,
  se = NULL,
  influence = NULL,
  CI_type = "percentile",
  level = 0.95,
  B_vals = length(boot_est),
  reps = 1L,
  format = "wide",
  seed = NULL
)

Value

If format = "wide", the function returns a data.frame

with reps rows per entry of B_vals, where each row contains confidence intervals for one sub-sample replication.

If format = "long", the function returns a data.frame with one row for each CI_type, each replication, and each entry of

B_vals, where each row contains a single confidence interval for one sub-sample replication.

If format = "wide-list", then the output will be structured as in

format = "wide" but will be wrapped in an unnamed list, which makes it easier to sore the output in a tibble, and will be assigned the class

"bootstrap_CIs".

Arguments

boot_est: vector of bootstrap replications of an estimator.
boot_se: vector of estimated standard errors from each bootstrap replication.
est: numeric value of the estimate based on the original sample. Required for CI_type = "normal", CI_type = "basic", CI_type = "student", and CI_type = "bias-corrected".
se: numeric value of the estimated standard error based on the original sample. Required for CI_type = "student".
influence: vector of empirical influence values for the estimator. Required for CI_type = "BCa".
CI_type: Character string or vector of character strings indicating types of confidence intervals to calculate. Options are "normal", "basic", "student", "percentile" (the default), "bias-corrected", or "BCa".
level: numeric value between 0 and 1 for the desired coverage level, with a default of 0.95.
B_vals: vector of sub-sample sizes for which to calculate confidence intervals. Setting B_vals = length(boot_est) (the default) will return bootstrap confidence intervals calculated on the full set of bootstrap replications. For B_vals < length(boot_est), confidence intervals will be calculated after sub-sampling (without replacement) the bootstrap replications.
reps: integer value for the number of sub-sample confidence intervals to generate when B_vals < length(boot_est), with a default of reps = 1.
format: character string controlling the format of the output. If format = "wide" (the default), then different types of confidence intervals will be returned in separate columns. If format = "long", then confidence intervals of different types will appear on different rows of dataset. If format = "wide-list", then different types of confidence intervals will be returned in separate columns and the result will be wrapped in an unnamed list.
seed: Single numeric value to which the random number generator seed will be set. Default is NULL, which does not set a seed.

Details

Confidence intervals are calculated following the methods described in Chapter 5 of Davison and Hinkley (1997). For basic non-parametric bootstraps, the methods are nearly identical to the implementation in boot.ci from the boot package.

References

Davison, A.C. and Hinkley, D.V. (1997). _Bootstrap Methods and Their Application_, Chapter 5. Cambridge University Press.

Examples

Run this code

# generate t-distributed data
N <- 50
mu <- 2
nu <- 5
dat <- mu + rt(N, df = nu)

# create bootstrap replications
f <- \(x) {
 c(
   M = mean(x, trim = 0.1),
   SE = sd(x) / sqrt(length(x))
 )
}

booties <- replicate(399, {
  sample(dat, replace = TRUE, size = N) |>
  f()
})

res <- f(dat)

# calculate bootstrap CIs from full set of bootstrap replicates
bootstrap_CIs(
  boot_est = booties[1,],
  boot_se = booties[2,],
  est = res[1],
  se = res[2],
  CI_type = c("normal","basic","student","percentile","bias-corrected"),
  format = "long"
)

# Calculate bias-corrected-and-accelerated CIs
inf_vals <- res[1] - sapply(seq_along(dat), \(i) f(dat[-i])[1])
bootstrap_CIs(
  boot_est = booties[1,],
  est = res[1],
  influence = inf_vals,
  CI_type = c("percentile","bias-corrected","BCa"),
  format = "long"
)

# calculate multiple bootstrap CIs using sub-sampling of replicates
bootstrap_CIs(
  boot_est = booties[1,],
  boot_se = booties[2,],
  est = res[1],
  se = res[2],
  CI_type = c("normal","basic","student","percentile","bias-corrected"),
  B_vals = 199,
  reps = 4L,
  format = "long"
)

# calculate multiple bootstrap CIs using sub-sampling of replicates,
# for each of several sub-sample sizes.
bootstrap_CIs(
  boot_est = booties[1,],
  boot_se = booties[2,],
  est = res[1],
  se = res[2],
  CI_type = c("normal","basic","student","percentile"),
  B_vals = c(49,99,199),
  reps = 4L,
  format = "long"
)

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