Classical interval estimation needs a sampling distribution, and the probability branch derives the ones that exist in closed form. For most statistics an analyst cares about, no such form exists. The sampling distribution of a Sharpe ratio, a maximum drawdown or a rank correlation is either unavailable or available only under assumptions the data violate.
How does the bootstrap work?
The bootstrap replaces the missing theory with the sample itself. Treat the observed data as the population, draw a resample of the same size with replacement, compute the statistic, and repeat ten thousand times. The spread of those ten thousand values estimates the spread of the statistic. Sort them and cut at the 2.5th and 97.5th percentiles, on a stated interpolation convention, and you have a percentile confidence interval at 95%.
Worked example 5 runs it on the twenty-quarter series' Sharpe ratio. The point estimate is 0.113649 per quarter. The delta-method interval built on Var(SR) ≈ (1 + SR²/2)/T gives a symmetric [−0.326, +0.553]; the bootstrap gives [−0.287, +0.763], wider and visibly asymmetric, with a lower arm of 0.400 and an upper arm of 0.649. The asymmetry is the information. A Sharpe ratio estimated from twenty quarters has a long right tail, so a symmetric interval reports the wrong shape of uncertainty even when its width is roughly right.
Three disciplines make a bootstrap admissible. State the seed, because the interval is a property of the resampling as well as of the data: the same computation at three seeds gives upper endpoints of 0.7626, 0.7330 and 0.7726, so the third decimal is noise. State B, because the Monte Carlo standard error of a 2.5% quantile at B = 10,000 is about 0.0016 in probability. And state the resampling unit, because drawing individual observations destroys any serial dependence the data had; block bootstraps exist for that reason, and the ordinary bootstrap silently assumes independence.
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How does the jackknife work?
The jackknife is the older, cheaper cousin. Leave out one observation, recompute, repeat n times. The n leave-one-out values give a bias estimate, (n − 1)(θ̄_jack − θ̂), and a standard error. On the same series the jackknife's bias estimate is +0.043543 and the bootstrap's is +0.040440: two independent routes agreeing that the raw Sharpe ratio is biased upward by about four hundredths. That agreement is worth more than either number alone.
Its second use is influence. Dropping the −21.40% quarter raises the Sharpe from 0.1136 to 0.3059; dropping the +15.30% quarter lowers it to 0.0435. One observation in twenty moves the headline statistic by 170%, which no confidence interval communicates.