On the Number of Bootstrap Simulations Required to Construct a Confidence Interval
Hall, Peter
Ann. Statist., Tome 14 (1986) no. 2, p. 1453-1462 / Harvested from Project Euclid
We make two points about the number, $B$ of bootstrap simulations needed to construct a percentile-$t$ confidence interval based on an $n$ sample from a continuous distribution: (i) The bootstrap's reduction of error of coverage probability, from $O(n^{-1/2})$ to $O(n^{-1})$, is available uniformly in $B$, provided nominal coverage probability is a multiple of $(B + 1)^{-1}$. In fact, this improvement is available even if the number of simulations is held fixed as $n$ increases. However, smaller values of $B$ can result in longer confidence intervals. (ii) In a large sample, the simulated statistic values behave like random observations from a continuous distribution, unless $B$ increases faster than any power of sample size. Only if $B$ increases exponentially quickly with $n$ is there a detectable effect due to discreteness of the bootstrap statistic.
Publié le : 1986-12-14
Classification:  Bootstrap,  confidence interval,  number of simulations,  62G15,  62E20
@article{1176350169,
     author = {Hall, Peter},
     title = {On the Number of Bootstrap Simulations Required to Construct a Confidence Interval},
     journal = {Ann. Statist.},
     volume = {14},
     number = {2},
     year = {1986},
     pages = { 1453-1462},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176350169}
}
Hall, Peter. On the Number of Bootstrap Simulations Required to Construct a Confidence Interval. Ann. Statist., Tome 14 (1986) no. 2, pp.  1453-1462. http://gdmltest.u-ga.fr/item/1176350169/