Statistics · Maths EE idea · Ambitious
Can resampling replace formulas?
A research question to start from
How well do bootstrap confidence intervals for a mean match the formula-based intervals, and when does the bootstrap fail?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
A modern method examined critically, with clear measures of success.
Mathematics you would need
- Sampling distributions
- Confidence intervals
- Resampling with replacement
- Coverage probability
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Explain the bootstrap idea mathematically.
- Compare coverage of bootstrap and t-intervals by simulation.
- Find and explain a failure case (for example the maximum).
Scope and difficulty
Ambitious. Ambitious; mostly simulation-based, so the explanation must be strong.
Pitfalls
- Code as the main content.
- No definition of coverage.
Where to start reading
Search a library catalogue or a university's open lecture notes for: bootstrap confidence interval coverage; bootstrap failure maximum. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).