When does the bootstrap give you the wrong answer?

hard

Answer

$It fails where the statistic depends on the extreme tail of the distribution, because resampling can never produce a value larger than the largest observation, so the maximum and near-extreme quantiles are badly estimated.$
$It fails with small samples, since the empirical distribution is a poor stand-in for the population and the intervals come out too narrow.$
$It fails when observations are dependent, which is the most common real-world violation: naive resampling of time series or clustered data destroys the correlation structure and understates variance badly, and you need a block or cluster bootstrap instead.$
$It also struggles with statistics that are not smooth functions of the data, such as the median in small samples with ties.$
$The general rule is that it substitutes computation for a distributional assumption, but not for independence.$

Check yourself — multiple choice

It is always valid
For extreme-tail statistics, very small samples, and dependent data where naive resampling destroys correlation — use block or cluster bootstraps for the latter
Only for means
It requires normality

The bootstrap replaces distributional assumptions but still assumes independence and adequate sample support.

#bootstrap#confidence-interval

215 interview questions in this topic.