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.

翻译：Bootstrap是一种广泛使用的技术，可用于估计给定估计量的性质，如其偏差和标准误。本文评估并比较了五种基于Bootstrap的置信区间构建方法：其中两种（正态法和学生化法）基于Bootstrap的标准误估计；另外两种（分位数法和改进法）基于参数估计量的估计分布；最后，考虑一种基于贝叶斯Bootstrap构建的区间，该区间依赖于可信区间的概念。通过蒙特卡洛模拟在不同情景下对这些方法进行比较，包括由copula模型诱导自相关的样本。结果还从覆盖率、中位区间长度以及本文提出的结合这两者的新指标角度进行了比较。结果表明，学生化法具有最佳覆盖率，但贝叶斯法所得到的区间最小。总体而言，所有方法均适用且表现出良好性能，即使在违反独立性假设的情景下也是如此。