Bootstrap Confidence Interval (Percentile)

Background

The percentile bootstrap is the universal confidence-interval tool: resample your data with replacement, recompute the statistic each time, take the $(\alpha/2, 1 - \alpha/2)$ quantiles of the bootstrap distribution. No parametric assumptions, no closed form needed.

Problem statement

Implement bootstrap_ci(data, stat_fn, n_bootstrap=2000, alpha=0.05, seed=0). For each bootstrap iteration, sample $n$ values from data with replacement, apply stat_fn, collect $B$ statistics, and return $(\text{lo}, \text{hi})$ at the $\alpha/2$ and $1 - \alpha/2$ percentiles.

Input

• data - sequence of values.
• stat_fn - function taking a sequence -> scalar.
• n_bootstrap - int >= 100.
• alpha - float in $(0, 1)$ (default $0.05$ for a 95% CI).
• seed - RNG seed.

Output

• (lo, hi) - tuple of plain Python floats.

Examples

Input: data=[1,2,3,4,5,6,7,8,9,10], stat_fn=mean
Output: CI roughly around mean ~ 5.5 with bounds about (4, 7)

Constraints

• Reproducible via seed.
• Return Python floats.

Notes

• Why percentile, not normal. No assumption that the statistic is normally distributed. Works for medians, quantiles, ratios, anything.