Bootstrap Resampling & Empirical CI

Non-parametric Bootstrap Resampling & Empirical Confidence Intervals (Efron) provides a distribution-free resampling algorithm to estimate standard errors and confidence intervals for non-linear, non-normal summary statistics (e.g. median, P95/P99 latency, ratio of means, Gini coefficients) lacking analytical closed-form asymptotic distributions; standard algorithm: 1) Uniform sampling with replacement: drawing $N$ observations from original sample size $N$ to form a synthetic bootstrap dataset; 2) Iterating $B=10,000$ times, re-computing target statistic $\hat{\theta}^{*b}$ per draw; 3) Formulating the empirical sampling distribution; 4) Deriving Confidence Intervals via Empirical Percentiles ($[\hat{\theta}_{\alpha/2}^*, \hat{\theta}_{1-\alpha/2}^*]$) or Bias-Corrected and Accelerated (BCa) intervals adjusting for skewness and estimation bias.

Non-normal metric hypothesis testing (P99 latency, user retention ratios, conversion funnels) and robust variance estimation.

Eliminates reliance on unrealistic Gaussian assumptions or asymptotic Central Limit Theorems on highly skewed, long-tailed business metrics.

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