You receive a pandas DataFrame and a statistic-producing function. Implement bootstrap and jackknife procedures to estimate uncertainty for that statistic, then explain when the two methods can be misleading. ### Constraints & Assumptions - Each row is an independent sampling unit unless you explicitly choose a grouped resampling unit. - The statistic function accepts a DataFrame and returns one numeric value. - Your implementation should be reproducible under a supplied random seed. - You may use percentile bootstrap intervals; explain limitations rather than claiming they are universally optimal. ### Clarifying Questions to Ask - What statistic is being estimated, and is it smooth or sensitive to extremes? - Are rows independent, or are observations clustered by user, region, or time? - How many resamples are required, and which confidence level should be returned? - Can the statistic fail or become undefined on some resamples? ### What a Strong Answer Covers - Bootstrap sampling with replacement at the correct observational unit and deterministic random-state handling. - A distribution of bootstrap estimates, standard error, and clearly labeled percentile interval. - Leave-one-out jackknife estimates, their mean, and the standard jackknife variance formula. - Correct handling of grouping, missing values, unstable statistics, and computational cost. - Discussion of bias, skewness, nonsmooth statistics, small samples, dependence, and more suitable variants when needed. ### Follow-up Questions 1. How would you bootstrap a user-level metric when each user has many rows? 2. Why can a naive row bootstrap fail for time-series data? 3. What is the difference between the bootstrap sample size and the number of bootstrap replications? 4. When would you prefer a block bootstrap or stratified bootstrap?