06. Bootstrapping

The sample as a proxy for the unknown population. Sample from said proxy population (i.e., the sample) to generate a sampling distribution. Bootstrap.

Artwork by @allison_horst.

Agenda

October 7, 2024

1. Review: logic of confidence intervals
2. Logic of bootstrapping (resample from the sample with replacement)
3. BS SE of a statistic

October 9, 2024

1. Normal CI using BS SE
2. Bootstrap-t (studentized) CIs
3. Percentile CIs
4. properties / advantages / disadvantages

Readings

• Class notes: Bootstrapping

• Baumer, Horton, and Kaplan (2021), The bootstrap (Chp 9.3) in Modern Data Science for R.

• Gareth, Witten, Hastie, and Tibshirani (2021), The Bootstrap (section 5.2) Introduction to Statistical Learning.

Reflection questions

• Why would anyone ever want to bootstrap?

• What are the differences between a normal CI with Boot SE, a Bootstrap-t CI, and a percentile interval?

• Why do we need to bootstrap twice for the Bootstrap-t CI?

• What makes a confidence interval procedure good?

Ethics considerations

• Why isn’t the bootstrap method a solution for the situation of small sample sizes?

• Why isn’t the bootstrap method a solution for the situation with biased / unrepresentative data?

• Consider a population with a maximum value (the parameter of interest). Will the sample max have a sampling distribution which is centered on the true maximum? Why or why not? [Quintessential example of how a statistic can be biased for the parameter.]

Slides

• In class slides for both 10/7/24 and 10/9/24.

• WU10 - standard errors

• WU11 - bootstrap t

Additional Resources

• StatKey applets which demonstrate bootstrapping.

• Confidence interval logic from the Rossman & Chance applets.

• The Role of Statistical Learning in Applied Statistics Daniela Witten talks to Rafa Irizarry June 15, 2020.

• Five ways to fix statistics, Nature Nov 28, 2017

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