Implement percentage RMSE and bootstrap its CI

Q: Implement percentage RMSE and bootstrap its CI

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Question

Given a CSV with columns [country, actual_revenue, predicted_revenue], define percentage RMSE as pRMSE = sqrt(mean_i((pred_i/actual_i − 1)^2)). a) Implement pRMSE carefully: handle zeros/negatives, optional country weights, and numerical stability. b) Implement a nonparametric n‑of‑n bootstrap to obtain a 95% CI for pRMSE; justify the choice of resample size and discuss when a stratified or cluster bootstrap is preferable. c) What is the exact probability that one bootstrap resample equals the original sample in exactly the same order? Provide the formula in terms of n and explain why it is typically tiny. d) Discuss limitations of bootstrapping this metric (heavy tails, dependence across countries) and mitigations.

Implement percentage RMSE and bootstrap its CI

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