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A SIMULATION STUDY OF BOOTSTRAP CONFIDENCE INTERV ALS FOR THE LOCATION OF ASYMMETRIC AND HEAVY TAILED DISTRIBUTIONS

Year 2013, Volume: 14 Issue: 3, 213 - 229, 04.05.2015

Abstract

Bootstrap methodology is a modern statistical tool which enables us makin g 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 tthe literature. In this study, the coverage accuracy of four most commonly used bootstrap confidence interval methods was assessed for  various asymmetr c  and  heavy  tailed  distributions with  an  exh austive 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.

References

  • 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.
  • Boos, D., Hughes-Oliver, J. (2000). How Large Does n Have to be for z and t Intervals?, American Statistician, 54(2), 121–128.
  • Carpenter, J., Bithell, J. (2000). Bootstrap Confidence Intervals: when, which, what? A Practical Guide for Medical Statisticians. Statistics in Medicine, 19, 1141–1164.
  • 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.
  • 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). Bootstrap Confidence Intervals, Statistical Science, 11(3), 189-212.
  • 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.
  • 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.
  • Özdemir, A. F., Wilcox, R.R. (2012). New Results on The Small-Sample Properties of some Robust Univariate Estimators of Location. Communications in Statistics - Simulation and Computation, 41(9), 1544-1556.
  • Serfling, R.J. (1980). Approximation Theorems of Mathematical Statistics. Newyork: Wiley.
  • Ted' Micceri's Web Site. http://www.freewebs.com/tedstats. Alıntı tarihi: 01.10.2012.
  • Wilcox, R.R. (2001). Fundamentals of Modern Statistical Methods. Springer-Verlag.
  • Wilcox, R.R. (2012). Introduction to Robust Estimation and Hypothesis Testing. 3rd Edition, Academic Press.
  • Zhou, X. H., Dinh, P. (2005). Nonparametric Confidence Intervals for The One and Two Sample Problems. Biostatistics, 6(2), 187 – 200.
  • Zhou, X. H., Gao, S. (2000). One-sided Confidence Intervals for Means of Positively Skewed Distributions. The American Statistician, 54(2), 100 – 104.

ASİMETRİK VE AĞIR KUYRUKLU DAĞILIMLARIN KONUM PARAMETRESİNİN BOOTSTRAP GÜVEN ARALIKLARI İÇİN BİR BENZETİM ÇALIŞMASI

Year 2013, Volume: 14 Issue: 3, 213 - 229, 04.05.2015

Abstract

References

  • 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.
  • Boos, D., Hughes-Oliver, J. (2000). How Large Does n Have to be for z and t Intervals?, American Statistician, 54(2), 121–128.
  • Carpenter, J., Bithell, J. (2000). Bootstrap Confidence Intervals: when, which, what? A Practical Guide for Medical Statisticians. Statistics in Medicine, 19, 1141–1164.
  • 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.
  • 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). Bootstrap Confidence Intervals, Statistical Science, 11(3), 189-212.
  • 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.
  • 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.
  • Özdemir, A. F., Wilcox, R.R. (2012). New Results on The Small-Sample Properties of some Robust Univariate Estimators of Location. Communications in Statistics - Simulation and Computation, 41(9), 1544-1556.
  • Serfling, R.J. (1980). Approximation Theorems of Mathematical Statistics. Newyork: Wiley.
  • Ted' Micceri's Web Site. http://www.freewebs.com/tedstats. Alıntı tarihi: 01.10.2012.
  • Wilcox, R.R. (2001). Fundamentals of Modern Statistical Methods. Springer-Verlag.
  • Wilcox, R.R. (2012). Introduction to Robust Estimation and Hypothesis Testing. 3rd Edition, Academic Press.
  • Zhou, X. H., Dinh, P. (2005). Nonparametric Confidence Intervals for The One and Two Sample Problems. Biostatistics, 6(2), 187 – 200.
  • Zhou, X. H., Gao, S. (2000). One-sided Confidence Intervals for Means of Positively Skewed Distributions. The American Statistician, 54(2), 100 – 104.
There are 24 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Engin Yıldıztepe

Abdullah Özdemir

Publication Date May 4, 2015
Published in Issue Year 2013 Volume: 14 Issue: 3

Cite

APA Yıldıztepe, E., & Özdemir, A. (2015). A SIMULATION STUDY OF BOOTSTRAP CONFIDENCE INTERV ALS FOR THE LOCATION OF ASYMMETRIC AND HEAVY TAILED DISTRIBUTIONS. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, 14(3), 213-229.
AMA Yıldıztepe E, Özdemir A. A SIMULATION STUDY OF BOOTSTRAP CONFIDENCE INTERV ALS FOR THE LOCATION OF ASYMMETRIC AND HEAVY TAILED DISTRIBUTIONS. AUJST-A. May 2015;14(3):213-229.
Chicago Yıldıztepe, Engin, and Abdullah Özdemir. “A SIMULATION STUDY OF BOOTSTRAP CONFIDENCE INTERV ALS FOR THE LOCATION OF ASYMMETRIC AND HEAVY TAILED DISTRIBUTIONS”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 14, no. 3 (May 2015): 213-29.
EndNote Yıldıztepe E, Özdemir A (May 1, 2015) A SIMULATION STUDY OF BOOTSTRAP CONFIDENCE INTERV ALS FOR THE LOCATION OF ASYMMETRIC AND HEAVY TAILED DISTRIBUTIONS. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 14 3 213–229.
IEEE E. Yıldıztepe and A. Özdemir, “A SIMULATION STUDY OF BOOTSTRAP CONFIDENCE INTERV ALS FOR THE LOCATION OF ASYMMETRIC AND HEAVY TAILED DISTRIBUTIONS”, AUJST-A, vol. 14, no. 3, pp. 213–229, 2015.
ISNAD Yıldıztepe, Engin - Özdemir, Abdullah. “A SIMULATION STUDY OF BOOTSTRAP CONFIDENCE INTERV ALS FOR THE LOCATION OF ASYMMETRIC AND HEAVY TAILED DISTRIBUTIONS”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 14/3 (May 2015), 213-229.
JAMA Yıldıztepe E, Özdemir A. A SIMULATION STUDY OF BOOTSTRAP CONFIDENCE INTERV ALS FOR THE LOCATION OF ASYMMETRIC AND HEAVY TAILED DISTRIBUTIONS. AUJST-A. 2015;14:213–229.
MLA Yıldıztepe, Engin and Abdullah Özdemir. “A SIMULATION STUDY OF BOOTSTRAP CONFIDENCE INTERV ALS FOR THE LOCATION OF ASYMMETRIC AND HEAVY TAILED DISTRIBUTIONS”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, vol. 14, no. 3, 2015, pp. 213-29.
Vancouver Yıldıztepe E, Özdemir A. A SIMULATION STUDY OF BOOTSTRAP CONFIDENCE INTERV ALS FOR THE LOCATION OF ASYMMETRIC AND HEAVY TAILED DISTRIBUTIONS. AUJST-A. 2015;14(3):213-29.