Description

The bootstrap is a computer-intensive statistical method introduced by Efron in 1979. It is a resampling technique for obtaining estimates of properties of statistical estimators without making assumptions about the underlying distribution of the data, e.g. to find standard errors of estimates, confidence intervals for unknown parameters, and other measures of accuracy. The bootstrap has received much attention over the past decades due to its simplicity and ability to adapt to general data structures. Some would say that it renders traditional statistical theory and methods redundant but of course "there ain't no such thing as a free lunch" and the challenge is to decide when the bootstrap provides the best practical solution to a problem.

“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)

Although the basic idea of the bootstrap is simple, the methodology needs to be tailored to the kind of data being modelled and to the specific statistical model being used. Demonstrating that the method performs reasonably in any particular application provides plenty of challenge for those drawn to the theory. There are many interesting specialist kinds of application that might be explored, including regression modelling, dependent data and time series, heavy-tailed data and extremes, spatial data and machine learning (bagging and boosting). A student taking the project may choose to specialise in the theory or in computation or in a particular application or to combine these aspects.

Meetings will be as a group during the first term. During the second term, meetings will usually be individual with the supervisor and may sometimes take place online if the supervisor is away from Durham.

Prerequisites

• Statistical Concepts II
• Monte Carlo II (recommended but not required)
• Familiarity with R

Corequisites

Statistical Methods III (recommended)

Resources

• The Wikipedia entry on "Bootstrapping (statistics)" and references therein.
• 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.