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Journals / Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :A-Uygulamalı Bilimler ve Mühendislik / 2013 / Cilt: 14 - Sayı: 3

A Simulation Study of Bootstrap Confidence Intervals for The Location of Asymmetric and Heavy Tailed Distributions

Asimetrik ve Ağır Kuyruklu Dağılımların Konum Parametresinin Bootstrap Güven Aralıkları için Bir Benzetim Çalışması

Engin YILDIZTEPE
ÖZDEMİR A. Fırat
Pages
213–229
Publication Date
2022-10-11
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In most of the cases, it has been found that the coverage accuracy of bootstrap percentile method is close to nominal for robust estimators of location.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Bootstrap methodology is a modern statistical tool which enables us making statistical inference when the sampling distribution of the estimator is not known.
📊
Key Findings & Data:Although the underlying idea is the same in all bootstrap methods, one might come across so many variations in the literature.
💡
Conclusion & Impact:In most of the cases, it has been found that the coverage accuracy of bootstrap percentile method is close to nominal for robust estimators of location.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

Bootstrap methodology is a modern statistical tool which enables us making statistical inference when the sampling distribution of the estimator is not known. Although the underlying idea is the same in all bootstrap methods, one might come across so many variations in the literature. In this study, the coverage accuracy of four most commonly used bootstrap confidence interval methods was assessed for various asymmetric and heavy tailed distributions with an exhaustive Monte Carlo simulation. In most of the cases, it has been found that the coverage accuracy of bootstrap percentile method is close to nominal for robust estimators of location.

Özet

Bootstrap yöntemi, kestiricinin örnekleme dağılımı bilinmediği durumlarda çıkarsama yapabilmemizi sağlayan modern bir istatistiksel araçtır. Tüm bootstrap yöntemlerinin temel fikri aynı olsa da literatürde farklı varyasyonları yer almaktadır. Bu çalışmada, detaylı bir Monte Carlo benzetimi ile asimetrik ve ağır kuyruklu dağılımlar için, yaygın olarak kullanılan dört bootstrap güven aralığı yönteminin kapsama oranı araştırılmıştır. Dayanıklı kestiriciler için yüzdelik bootstrap yöntemiyle elde edilen kapsama oranları birççok durum için nominal değere yakın bulunmuştur.

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Cite This Article

YILDIZTEPE, E., Fırat, Ö. A. (2022). A Simulation Study of Bootstrap Confidence Intervals for The Location of Asymmetric and Heavy Tailed Distributions. Anadolu Üniversitesi Bilim ve Teknoloji Dergisi :A-Uygulamalı Bilimler ve Mühendislik, Cilt: 14 - Sayı: 3, 213–229. https://ajindex.com/articles/438388

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References (9)

  1. Banik, S., Kibria, B.M.G. (2010). Comparison of some Parametric and Nonparametric Type One Sample Confidence Intervals for Estimating the Mean of a Positively Skewed Distribution. Communications in Statistics - Simulation and Computation, 39(2), 361-389.
  2. Boos, D., Hughes-Oliver, J. (2000). How Large Does n Have to be for z and t Intervals?, American Statistician, 54(2), 121-128.
  3. Carpenter, J., Bithell, J. (2000). Bootstrap Confidence Intervals: when, which, what? A Practical Guide for Medical Statisticians. Statistics in Medicine, 19, 1141-1164.
  4. Chernick, M.R. (2008). Bootstrap Methods: a Guide for Practitioners and Researchers. 2nd Edition, John Wiley & Sons, New Jersey. Davison, A.C., Hinkley, D. V. (1997). Bootstrap Methods and Their Application. Cambridge University Press.
  5. Davison, A.C., Hinkley, D.V., Young, G.A. (2003). Recent Developments in Bootstrap Methodology. Statistical Science, 18(2), 141 - 157. DiCiccio, T.J., Efron. B. (1996).
  6. Bootstrap Confidence Intervals, Statistical Science, 11(3), 189-212.
  7. Efron, B. (1979). Bootstrap Methods: Another Look at The Jackknife. The Annals of Statistics, 7(1), 1- 26. Efron, B. (1981). Nonparametric Standard Errors and Confidence Intervals. The Canadian Journal of Statistics, 9(2), 139 - 158. Efron, B. (1987). Better Bootstrap Confidence Intervals. Journal of The American Statistical Association, 82(397), 171 - 200. Efron, B., Tibshirani, R. (1986). Bootstrap Methods for Standard Errors, Confidence Intervals, and other Measures of Statistical Accuracy. Statistical Science 1(1), 54 - 77. Efron, B., Tibshirani R. (1993). An Introduction to The Bootstrap. Chapman and Hall, London. Hoaglin, D. C. (1985). Summarizing Shape Numerically: The g-and-h Distributions. In D. Hoaglin, F. Mosteller, & J. Tukey (eds.), Exploring Data Tables, Trends, and Shapes. Wiley, New York. Huber, P.J. (1981). Robust Statistics. New York: Wiley. Kuonen, D. (2005). Studentized Bootstrap Confidence Intervals Based on Mestimates. Journal of Applied Statistics, 32(5), 443-460.
  8. Nankervis, J.C. (2005). Computational Algorithms for Double Bootstrap Confidence Intervals. Computational Statistics & Data Analysis, 49, 461 - 475. Ng, H.K.T., Filardo, G., Zheng, G. (2008). Confidence Interval Estimating Procedures for Standardized Incidence Rates. Computational Statistics and Data Analysis, 52, 3501-3516.
  9. Özdemir, A. F., Wilcox, R.R. (2012). New Results on The Small-Sample Properties of some Robust Univariate Estimators of Location. Communications