| ExpandProbs {resample} | R Documentation |
Calculate modified probabilities for more accurate confidence intervals
Description
Compute modified quantiles levels, for more accurate confidence intervals. Using these levels gives sider intervals, with closer to desired coverage.
Usage
ExpandProbs(probs, n)
Arguments
probs |
vector of numerical values between 0 and 1. |
n |
number of observations. |
Details
Bootstrap percentile confidence interval for a sample mean correspond roughly to
\bar x \pm z_\alpha \hat\sigma
instead of
\bar x \pm t_{\alpha,n-1} s
where
\hat\sigma = \sqrt{(n-1)/n s}
is like s but computed using a divisor of n instead of n-1. Similarly for other statistics, the bootstrap percentile interval is too narrow, typically by roughly the same proportion.
This function finds modified probability levels probs2, such that
z_{\mbox{probs2}} \sqrt{(n-1)/n} = t_{\mbox{probs}, n-1}
z_probs2 sqrt((n-1)/n) = t_probs,n-1 so that for symmetric data, the bootstrap percentile interval approximately matches the usual $t$ confidence interval.
Value
A vector like probs, but with values closer to 0 and 1.
Author(s)
Tim Hesterberg timhesterberg@gmail.com,
https://www.timhesterberg.net/bootstrap-and-resampling
References
This discusses the expanded percentile interval: Hesterberg, Tim (2014), What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics Curriculum, https://arxiv.org/abs/1411.5279.
See Also
Examples
probs <- c(0.025, 0.975)
n <- c(5, 10, 20, 40, 100, 200, 1000)
outer(probs, n, ExpandProbs)