Bootstrap confidence intervals: A comparative simulation study

TL;DR

This study compares five bootstrap methods for constructing confidence intervals through extensive simulations, evaluating their coverage, interval length, and robustness across various data scenarios, including autocorrelated samples.

Contribution

It provides a comprehensive comparison of bootstrap confidence interval methods, introducing a new combined indicator for performance evaluation and including Bayesian bootstrap in the analysis.

Findings

Studentized method has the best coverage rate.

Bayesian bootstrap produces the smallest intervals.

All methods perform well even with dependent data.

Abstract

Bootstrap is a widely used technique that allows estimating the properties of a given estimator, such as its bias and standard error. In this paper, we evaluate and compare five bootstrap-based methods for making confidence intervals: two of them (Normal and Studentized) based on the bootstrap estimate of the standard error; another two (Quantile and Better) based on the estimated distribution of the parameter estimator; and finally, considering an interval constructed based on Bayesian bootstrap, relying on the notion of credible interval. The methods are compared through Monte Carlo simulations in different scenarios, including samples with autocorrelation induced by a copula model. The results are also compared with respect to the coverage rate, the median interval length and a novel indicator, proposed in this paper, combining both of them. The results show that the Studentized method has the best coverage rate, although the smallest intervals are attained by the Bayesian method. In general, all methods are appropriate and demonstrated good performance even in the scenarios violating the independence assumption.