A Three-step Method for Choosing the Number of Bootstrap Repetitions

Econometrica · 2000 · Volume 68 · Issue 1

Abstract

This paper considers the problem of choosing the number of bootstrap repetitionsBfor bootstrap standard errors, confidence intervals, confidence regions, hypothesis tests,p-values, and bias correction. For each of these problems, the paper provides a three-step method for choosingBto achieve a desired level of accuracy. Accuracy is measured by the percentage deviation of the bootstrap standard error estimate, confidence interval length, test's critical value, test'sp-value, or bias-corrected estimate based onBbootstrap simulations from the corresponding ideal bootstrap quantities for whichB=∞. The results apply quite generally to parametric, semiparametric, and nonparametric models with independent and dependent data. The results apply to the standard nonparametric iid bootstrap, moving block bootstraps for time series data, parametric and semiparametric bootstraps, and bootstraps for regression models based on bootstrapping residuals. Monte Carlo simulations show that the proposed methods work very well.

Keywords

Bias correction, bootstrap, bootstrap repetitions, confidence interval, hypothesis test, p-value, simulation, standard error estimate.

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