Improving the performance of bootstrap Edgeworth-based confidence interval for the mean of positively skewed distributions

Veljković, Kristina (author)

The mean can be an important metric, even when the data distribution is asymmetric. Current confidence intervals for the population mean do not attain the nominal confidence level for small to medium samples drawn from skewed distributions, except for the recently introduced bootstrap Edgeworth-based confidence interval. The limitation of the new method is its potential to produce long intervals for small samples. In this study, we explored various variants of this confidence interval that utilize different estimators of skewness and excess kurtosis. We assessed their performance by analyzing the coverage probability, mean interval length and the coefficient of variation of the length, using small to medium random samples drawn from a range of positively skewed distributions. The performance of four best-performing variants was compared to the bootstrap t, percentile, BC, and BCa confidence intervals. The improved bootstrap Edgeworth-based confidence interval demonstrated superior performance compared to other bootstrap confidence intervals regarding coverage probability, making it a strong recommendation for practical application.

• Language: English
• Keywords: bootstrap, confidence interval, Edgeworth expansion, kurtosis, skewness
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FRI - Faculty of Computer and Information Science
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: Str. 1-38
• Numbering: Vol. , no.
• PID: 20.500.12556/RUL-185007
• UDC: 519.22:519.233
• ISSN on article: 0361-0918
• DOI: 10.1080/03610918.2026.2688384
• COBISS.SI-ID: 285004803
• Publication date in RUL: 20.07.2026

Record is a part of a journal

• Title: Communications in statistics : Simulation and computation
• Shortened title: Commun. stat., Simul. comput.
• Publisher: Taylor & Francis
• ISSN: 0361-0918
• COBISS.SI-ID: 1639701

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: bootstrap, interval zaupanja, Edgeworthov razvoj, sploščenost, asimetrija