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Calculate normal bootstrap confidence interval

Source: R/norm_ci.R
norm_ci.Rd

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

Usage

norm_ci(
  t0,
  t,
  conf = 0.95,
  h = function(t) t,
  hinv = function(t) t,
  no_bias = FALSE
)

Arguments

t0

Original statistic.

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.

no_bias

Logical. If TRUE intervals are centered around the original estimates (bias is ignored). Default is FALSE.

Value

A matrix with four columns:

  • conf: confidence level

  • ll: lower confidence limit

  • ul: lower confidence limit

Details

$$CI_{norm} = \left[\hat{\theta} - \text{Bias}_{\text{boot}} - \text{SE}_{\text{boot}} \times z_{1-\alpha/2}, \hat{\theta} - \text{Bias}_{\text{boot}} + \text{SE}_{\text{boot}} \times z_{1-\alpha/2} \right]$$

where \(z_{1-\alpha/2}\) is the \(1-\alpha/2\) quantile of the standard normal distribution.

Note

This function is adapted from the function norm.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(), perc_ci()

Examples

set.seed(123)
boot_reps <- rnorm(1000)
t0 <- mean(boot_reps)

# Normal-based CI
norm_ci(t0, boot_reps, conf = 0.90)
#>      conf        ll       ul
#> [1,]  0.9 -1.615065 1.647321

# Without bias correction
norm_ci(t0, boot_reps, conf = 0.90, no_bias = TRUE)
#>      conf        ll       ul
#> [1,]  0.9 -1.615065 1.647321