Description Usage Arguments Details Value Author(s) References See Also Examples

Compute modified quantiles levels, for more accurate confidence intervals. Using these levels gives sider intervals, with closer to desired coverage.

1 | ```
ExpandProbs(probs, n)
``` |

`probs` |
vector of numerical values between 0 and 1. |

`n` |
number of observations. |

Bootstrap percentile confidence interval for a sample mean correspond roughly to

*xbar +- z_alpha sigmaHat*

instead of

*xbar +- t_alpha,n-1 s*

where

*sigmaHat = 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}} √{(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.

A vector like `probs`

, but with values closer to 0 and 1.

Tim Hesterberg timhesterberg@gmail.com,

http://www.timhesterberg.net/bootstrap

This discusses the expanded percentile interval: Hesterberg, Tim (2014), What Teachers Should Know about the Bootstrap: Resampling in the Undergraduate Statistics Curriculum, http://arxiv.org/abs/1411.5279.

1 2 3 | ```
probs <- c(0.025, 0.975)
n <- c(5, 10, 20, 40, 100, 200, 1000)
outer(probs, n, ExpandProbs)
``` |

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