Track 7 · Estimation and Confidence Intervals · Lesson 10 of 10
Bootstrap intervals
Build a percentile bootstrap interval by resampling, and judge when the bootstrap can and cannot be trusted.
An insurer wants a confidence interval for the median claim size. There is no simple formula for the standard error of a median, and claim amounts are wildly skewed, with one claim of 480 000 SAR. The bootstrap lets the computer build the sampling distribution from the data themselves.
Every interval so far needed a formula for the standard error and a known shape (normal or t) for the sampling distribution. For a median, a trimmed mean, a ratio or a correlation in skewed data, such formulas are awkward or unavailable.
The bootstrap (Efron, 1979) replaces theory with computation. The idea: we cannot draw new samples from the population, but the sample is our best picture of the population — so draw new samples from the sample.
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It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Describe and carry out the percentile bootstrap: resample with replacement, recompute, take percentiles
- Use the bootstrap for statistics without a simple standard-error formula, such as the median
- Recognise where the bootstrap fails: tiny samples, extremes, biased samples, dependent data
- Report B and the seed, and distinguish simulation noise from sampling uncertainty