An Introduction to Bootstrap Methods

TLDR

Bootstrap methods reuse samples to estimate standard errors and confidence intervals, offering fewer assumptions and greater accuracy than conventional techniques. This introduction applies bootstrap concepts to regression analysis. The authors compare two bootstrap resampling forms in regression, illustrating differences with examples involving outliers, heteroscedasticity, robust estimators, indirect effects, and various confidence‑interval approaches, and provide computational guidelines.

Abstract

Bootstrap methods are a collection of sample re-use techniques designed to estimate standard errors and confidence intervals. Making use of numerous samples drawn from the initial observations, these techniques require fewer assumptions and offer greater accuracy and insight than do standard methods in many problems. After presenting the underlying concepts, this introduction focuses on applications in regression analysis. These applications contrast two forms of bootstrap resampling in regression, illustrating their differences in a series of examples that include outliers and heteroscedasticity. Other regression examples use the bootstrap to estimate standard errors of robust estimators in regression and indirect effects in path models. Numerous variations of bootstrap confidence intervals exist, and examples stress the concepts that are common to the various approaches. Suggestions for computing bootstrap estimates appear throughout the discussion, and a section on computing suggests several broad guidelines.