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Investigating the Significance of a Correlation Coefficient using Bootstrap Estimates

Year 2019, Volume: 14 Issue: 1, 77 - 88, 31.05.2019
https://doi.org/10.29233/sdufeffd.460768

Abstract

Resampling
methods offers effective estimates of parameters and its asymptotic
distribution. In this study, it is
recommended to use the bootstrap method as an alternative to the classical and
knife (one exclusion procedure) test statistics in evaluating the significance
of the Pearson correlation coefficient by applying the bootstrap method to the
simple linear regression model.  This
procedure provides an effective alternative to test the significance of the
Pearson correlation coefficient. In the application, the model parameters,
standard errors, Pearson coefficients of correlation, bias and % 95 confidence
intervals belonging to bootstrap and jackknife methods in estimated with the
help of a real data and the obtained results are interpreted. As a result, the
test statistic obtained by the bootstrap method is proposed as an alternative
to the classical and jackknife test statistics.

References

  • M.R. Chernick, Bootstrap Methods a Guide for Practitioners and Researchers. 2nd ed; John Wiley & Sons Inc, New Jersey, 2008
  • B. Efron, “Bootstrap Method; Another Look at Jackknife,” Annals of Statistics, 7, 1-26, 1979.
  • D.A. Freedman, “Bootstrapping Regression Models,” Annals of Statistics, 1 (6), 1218-1228, 1981.
  • C. F. J. Wu, “Jackknife, Bootstrap and other Resampling Methods in Regression Analysis,” Annals of Statistics, 14 (4), 1261-1290, 1986.
  • Z. Y. Algamal, K. B. Rasheed, “Re-sampling in Linear Regression Model Using Jackknife and Bootstrap,” Iraqi Journal of Statistical Science, 18, 59-73, 2010.
  • A. Akpanta, I. Okorie, “Investigating the Significance of a Correlation Coefficient using Jackknife Estimates,” International Journal of Sciences: Basic and Applied Research (IJSBAR), 22 (2), 2015.
  • M. H. Quenouille, “Approximate tests of correlation in time series,” Journal of the Royal Statistical Society, 11, 18-44, 1949.
  • M. H. Quenouille, “Notes on bias in estimation,” Biometrika, 61, 353-360, 1956.
  • J. W. Tukey, “Bias and confidence in not-quite large sample,” Ann. Math. Stat., 29, 614, 1958.
  • S. Lohr, Sampling: design and analysis. Nelson Education, 2009.
  • H. Friedl, E. Stampfer, “Jackknife Resampling”, Encyclopaedia of Econometrics. 2, 1089-1098, 2002.
  • S. Sahinler, D. Topuz, “Bootstrap and Jackknife Resampling Algorithms for Estimation of Regression Parameters,” Journal of Applied Quantitative Methods, 2 (2), 188-199, 2007.
  • H. Abdi, J.L Williams, Jackknife. In Neil Salkind (Ed.), Encyclopaedia of Research Design. Thousand Oaks, CA: Sage, 2010.
  • B. Efron, “Bootstrap Method; another Look at Jackknife,” Annals of Statistics, 7 (1), 26, 1979.
  • M. R. Chernıck, Bootstrap methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 619, 2008
  • N. Hamajıma, “Methods for Statistical Inferences,” Biotheraphy-Tokyo, 13, 739-744, 1999.
  • R. Stine, Modern Methods of Data Analysis, by John Fox, Scotland: 325- 373, 1990.
  • N. Barker, “A Practical İntroduction to The Bootstrap Using The Sas System”. In SAS Conference Proceedings: Phuse 2005: Heidelberg, Germany SAS
  • D. Okutan, Bootstrap Yönteminin Regresyon Analizinde Kullanımı ve Diğer Yöntemlerle Karşılaştırılması. Ege Üniversitesi Fen Bilimleri Enstitüsü Yüksek Lisans Tezi, İzmir, 2009.
  • J. Fox, Applied Regression Analysis, Linear Models and Related Methods. Sage Publications Inc., 1997.
  • D. Topuz, Regresyonda Yeniden Örnekleme Yöntemlerinin Karşılaştırmalı Olarak İncelenmesi. Yüksek Lisans Tezi, Niğde, 2002.
  • Sperman's Correlation. Available: http://www.statstutor.ac.uk/resources/uploaded/spearmans.pdf.

Bootstrap Tahminini Kullanarak Pearson Korelasyon Katsayısının Önemliliğinin Araştırılması

Year 2019, Volume: 14 Issue: 1, 77 - 88, 31.05.2019
https://doi.org/10.29233/sdufeffd.460768

Abstract

Yeniden örnekleme yöntemleri
parametrelerin etkili tahminlerini ve asimptotik dağılımlarını sunar. Bu çalışmada, basit doğrusal regresyon
modeline bootstrap yöntemi uygulanarak Pearson korelasyon katsayısının
anlamlılığının değerlendirilmesinde klasik ve çakı (birini dışarıda bırak
işlemi)  test istatistiklerine alternatif
olarak bootstrap yönteminin kullanılması önerilmektedir. Bu prosedür Pearson
korelasyon katsayısının anlamlılığını test etmek için etkili bir alternatif
sağlar. Uygulamada bootstrap ve çakı yöntemlerine ait model parametreleri,
standart hatalar, Pearson korelasyon katsayısı, yanlılık ve %95 güven aralığı
gerçek bir veri yardımıyla elde edilerek sonuçlar yorumlanmıştır. Sonuçta,
bootstrap yöntemi ile elde edilen test istatistiği, klasik ve çakı tabanlı test
istatistiğine alternatif bir yöntem olarak önerilmiştir.

References

  • M.R. Chernick, Bootstrap Methods a Guide for Practitioners and Researchers. 2nd ed; John Wiley & Sons Inc, New Jersey, 2008
  • B. Efron, “Bootstrap Method; Another Look at Jackknife,” Annals of Statistics, 7, 1-26, 1979.
  • D.A. Freedman, “Bootstrapping Regression Models,” Annals of Statistics, 1 (6), 1218-1228, 1981.
  • C. F. J. Wu, “Jackknife, Bootstrap and other Resampling Methods in Regression Analysis,” Annals of Statistics, 14 (4), 1261-1290, 1986.
  • Z. Y. Algamal, K. B. Rasheed, “Re-sampling in Linear Regression Model Using Jackknife and Bootstrap,” Iraqi Journal of Statistical Science, 18, 59-73, 2010.
  • A. Akpanta, I. Okorie, “Investigating the Significance of a Correlation Coefficient using Jackknife Estimates,” International Journal of Sciences: Basic and Applied Research (IJSBAR), 22 (2), 2015.
  • M. H. Quenouille, “Approximate tests of correlation in time series,” Journal of the Royal Statistical Society, 11, 18-44, 1949.
  • M. H. Quenouille, “Notes on bias in estimation,” Biometrika, 61, 353-360, 1956.
  • J. W. Tukey, “Bias and confidence in not-quite large sample,” Ann. Math. Stat., 29, 614, 1958.
  • S. Lohr, Sampling: design and analysis. Nelson Education, 2009.
  • H. Friedl, E. Stampfer, “Jackknife Resampling”, Encyclopaedia of Econometrics. 2, 1089-1098, 2002.
  • S. Sahinler, D. Topuz, “Bootstrap and Jackknife Resampling Algorithms for Estimation of Regression Parameters,” Journal of Applied Quantitative Methods, 2 (2), 188-199, 2007.
  • H. Abdi, J.L Williams, Jackknife. In Neil Salkind (Ed.), Encyclopaedia of Research Design. Thousand Oaks, CA: Sage, 2010.
  • B. Efron, “Bootstrap Method; another Look at Jackknife,” Annals of Statistics, 7 (1), 26, 1979.
  • M. R. Chernıck, Bootstrap methods: A Guide for Practitioners and Researchers. John Wiley & Sons, 619, 2008
  • N. Hamajıma, “Methods for Statistical Inferences,” Biotheraphy-Tokyo, 13, 739-744, 1999.
  • R. Stine, Modern Methods of Data Analysis, by John Fox, Scotland: 325- 373, 1990.
  • N. Barker, “A Practical İntroduction to The Bootstrap Using The Sas System”. In SAS Conference Proceedings: Phuse 2005: Heidelberg, Germany SAS
  • D. Okutan, Bootstrap Yönteminin Regresyon Analizinde Kullanımı ve Diğer Yöntemlerle Karşılaştırılması. Ege Üniversitesi Fen Bilimleri Enstitüsü Yüksek Lisans Tezi, İzmir, 2009.
  • J. Fox, Applied Regression Analysis, Linear Models and Related Methods. Sage Publications Inc., 1997.
  • D. Topuz, Regresyonda Yeniden Örnekleme Yöntemlerinin Karşılaştırmalı Olarak İncelenmesi. Yüksek Lisans Tezi, Niğde, 2002.
  • Sperman's Correlation. Available: http://www.statstutor.ac.uk/resources/uploaded/spearmans.pdf.
There are 22 citations in total.

Details

Primary Language Turkish
Subjects Mathematical Sciences
Journal Section Makaleler
Authors

Tolga Zaman 0000-0001-8780-3655

Kamil Alakuş 0000-0001-8780-3655

Publication Date May 31, 2019
Published in Issue Year 2019 Volume: 14 Issue: 1

Cite

IEEE T. Zaman and K. Alakuş, “Bootstrap Tahminini Kullanarak Pearson Korelasyon Katsayısının Önemliliğinin Araştırılması”, Süleyman Demirel University Faculty of Arts and Science Journal of Science, vol. 14, no. 1, pp. 77–88, 2019, doi: 10.29233/sdufeffd.460768.