Abstract

Confidence intervals for the population variance in the presence of outliers or spikes in the distribution of a variable of interest are topics that have not been investigated in depth previously. Results derived from a first Monte Carlo simulation study reveal the limitations of the customary confidence interval for the population variance when the underlying assumptions are violated, and the use of alternative confidence intervals is thus justified. We suggest confidence intervals based on the rescaled bootstrap method for many reasons. First, this is a simple technique that can be easily applied in practice. Second, it is free of probabilistic distributions. Finally, it can be easily applied to the cases of finite populations and samples selected from complex sampling designs. Results derived from a second Monte Carlo simulation study indicate that the suggested confidence intervals have desirable coverage rates with smaller average widths. Accordingly, an advantage of the suggested confidence intervals is that they offer a good compromise between simplicity and desirable properties. The various simulation studies are based on different scenarios that may arise in practice, such as the presence of outliers or spikes, and the fact that the underlying assumptions of the customary confidence interval are violated.

摘要

在感兴趣的变量分布中存在异常值或尖峰时，总体方差的置信区间是以前没有深入研究过的主题。从第一个蒙特卡洛模拟研究得出的结果揭示了当基本假设被违反时总体方差的习惯置信区间的局限性，因此使用替代置信区间是合理的。出于多种原因，我们建议基于重新调整的引导程序方法的置信区间。首先，这是一种可以轻松应用于实践的简单技术。其次，它不受概率分布的影响。最后，它可以很容易地应用于从复杂抽样设计中选择的有限总体和样本的情况。第二次蒙特卡罗模拟研究得出的结果表明，建议的置信区间具有理想的覆盖率和较小的平均宽度。因此，建议的置信区间的一个优点是它们在简单性和所需属性之间提供了良好的折衷。各种模拟研究基于实践中可能出现的不同场景，例如异常值或尖峰的存在，以及违反惯常置信区间的基本假设的事实。