Resampling your own data to estimate how good your point-estimator is, and to reduce its bias. In general an intuitive technique. However, gets tricky for e.g. dependent data. For a handy crib sheet for bootstrap failure modes, see Thomas Lumley, When the bootstrap doesn’t work.

In the classical mode, this is a frequentist technique without an immediate Bayesian interpretation.

Commonly credited as being invented by B. Efron (1979) and theoretically justified by Gine and Zinn (1990).

## Teaching

## Bootstrap bias correction

As opp variance estimation. NBD; Bootstrap is notionally telling you the sampling distribution. 🏗

## Bootstrap for dependent data

e.g., as presaged, time series. Parametric bootstrap would be the logical default choice, right? When does that work?

## Causal bootstrap

Now a thing! (Imbens and Menzel 2021)

## As a Bayesian method

There is absolutely a Bayesian bootstrap if you think hard enough about it, it turns out. Several, really. Rubin (1981) derived a Bayesian version. See Lyddon, Holmes, and Walker (2019) for a modern update, and Rasmus Bååth for a diagrammed explanation of the points of contact with frequentist bootstrap and some other things.

## Pedagogic

Tim Hesterberg’s teaching notes:

## References

*Molecular Biology and Evolution*20 (2): 255–66.

*arXiv:0901.3202 [Cs, Stat]*.

*The Annals of Statistics*49 (1): 486–507.

*Journal of Econometrics*108 (2): 317–42.

*Statistical Science*17 (1): 52–72.

*Computational Statistics & Data Analysis*31 (3): 295–310.

*Sociological Methods & Research*33 (2): 261–304.

*Biometrika*102 (1): 203–14.

*Probability Theory and Related Fields*107 (2): 197–217.

*Journal of the Korean Statistical Society*40 (4): 379–81.

*Statistical Science*11 (3): 189–212.

*The Annals of Statistics*7 (1): 1–26.

*Biometrika*68 (3): 589–99.

*The Annals of Applied Statistics*6 (4): 1971–97.

*arXiv:1905.08737 [Stat]*, May.

*Algorithms*14 (1): 11.

*Annals of Probability*18 (2): 851–69.

*arXiv:1907.12116 [Cs, Math, Stat]*, July.

*Journal of the Korean Statistical Society*40 (4): 383–86.

*Journal of Econometrics*119 (1): 199–219.

*Resampling Methods: A Practical Guide to Data Analysis*. Birkhäuser Basel.

*The Annals of Statistics*24 (5): 1914–33.

*arXiv:1711.00813 [Stat]*, November.

*The Annals of Statistics*20 (2): 695–711.

*Handbook of Econometrics*, 4:2341–81. Elsevier.

*Biometrika*82 (3): 561–74.

*International Statistical Review*71 (2): 435–59.

*Wiley Interdisciplinary Reviews: Computational Statistics*3 (6): 497–526.

*Bootstrap Methods and Their Application*. Cambridge ; New York, NY, USA: Cambridge University Press.

*The Annals of Statistics*49 (3): 1460–88.

*The Annals of Statistics*17 (3): 1217–41.

*Statistics & Probability Letters*18 (5): 405–13.

*Probability Theory and Related Fields*121: 73–97.

*Resampling Methods for Dependent Data*. New York: Springer.

*Statistical Science*11 (3): 221–23.

*Biometrika*106 (2): 465–78.

*IEEE Transactions on Neural Networks*12 (6): 1278–87.

*arXiv:1409.4317 [Math, Stat]*, September.

*Statistical Science*18 (2): 219–30.

*Journal of the American Statistical Association*89 (428): 1303–13.

*Econometric Reviews*23 (1): 53–70.

*Journal of Time Series Analysis*30 (2): 167–78.

*Annals of Statistics*9 (1): 130–34.

*Clinical Psychological Science*7 (4): 778–93.

*American Scientist*98 (3): 186.

*Journal of the American Statistical Association*91 (434): 655–65.

*Statistica Sinica*7: 375–94.

*Journal of the Royal Statistical Society. Series B (Methodological)*39 (1): 44–47.

*arXiv:1506.06266 [Math, Stat]*, June.

*Water Resources Research*32 (6): 1875–82.

*Journal of Econometrics*133 (2): 579–99.

## No comments yet. Why not leave one?