ExpandProbs
Calculate modified probabilities for more accurate confidence intervals
Compute modified quantiles levels, for more accurate confidence intervals. Using these levels gives sider intervals, with closer to desired coverage.
- Keywords
- htest, nonparametric
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.
References
This discusses the expanded percentile interval:
Hesterberg, Tim (2014), What Teachers Should Know about the
Bootstrap: Resampling in the Undergraduate Statistics Curriculum,
See Also
Examples
probs <- c(0.025, 0.975)
n <- c(5, 10, 20, 40, 100, 200, 1000)
outer(probs, n, ExpandProbs)