Description

Resampling methods are a class of computer-intensive statistical techniques that involve repeatedly drawing samples from the observed data — with or without replacement — to assess the variability of estimators, test hypotheses, or estimate confidence intervals. These approaches provide flexible alternatives to classical analytical methods, particularly in settings where standard distributional assumptions are difficult to justify or verify, making them especially powerful in complex or non-standard applications.

The bootstrap, introduced by Efron in 1979, is the most widely known resampling method. It allows us to approximate the sampling distribution of a wide range of statistics by drawing samples with replacement from the original dataset. Other resampling techniques include the jackknife, which systematically omits observations to estimate bias and variance, and permutation tests, which generate null distributions by rearranging data labels.

“The bootstrap has shown us how to use the power of the computer and iterated calculations to go where theoretical calculations cannot, which introduces a different way of thinking about all of statistics.” (G. Casella, 2003)

Resampling methods have received considerable attention due to their conceptual simplicity, broad applicability, and compatibility with modern computing. There are many interesting topics to explore in this area. Here are just a few:

• Resampling for uncertainty estimation (e.g., estimating standard errors, confidence intervals, and bias)
• Resampling in dependent and structured Data (e.g., time series, spatial data, or clustered observations)
• Resampling in survival and censored Data (e.g., Kaplan–Meier, Cox models, censored observations)
• Permutation-based inference (e.g., testing for independence, group differences, or association)
• Resampling in machine learning and prediction (e.g., bagging, boosting, model selection, cross-validation)
• Resampling in complex or heavy-tailed data (e.g., skewed distributions, extreme values, small samples)

Prerequisites

• Statistical Inference
• Statistical Modelling or Data Science and Statistical Computing
• Familiarity with the statistical software R

References

• Efron, B. Bootstrap Methods: Another Look at the Jackknife. Ann. Statist. 7, 1-26, 1979.
• Efron, B. and Tibshirani, R. Bootstrap Methods for Standard Errors, Confidence Intervals, and Other Measures of Statistical Accuracy. Statist. Sci. 1, 54-75, 1986.
• Efron, B. Censored Data and the Bootstrap. Journal of the American Statistical Association, 76, 312- 319, 1981.
• Lahiri, S.N. Resampling Methods for Dependent Data. Springer Verlag Inc, 2003.
• Davison, A.C. and Hinkley, D.V. Bootstrap Methods and Their Application. Cambridge University Press, 1997.
• Efron, B. and Tibshirani, R. An Introduction to the Bootstrap. Chapman & Hall, 1993.
• Breiman, L. Bagging predictors. Machine Learning. 24, 123–140, 1996. 
• Tukey, J.W. Bias and Confidence in Not Quite Large Samples. Annals of Mathematical Statistics, 29, 614, 1958.
• Good, P. Permutation, Parametric, and Bootstrap Tests of Hypotheses (3rd ed.). Springer, 2005.
• Shao, J. & Tu, D. The Jackknife and Bootstrap. Springer-Verlag, 1995.