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PARAMETER ESTIMATION FOR LINEAR REGRESSION USING BOOTSTRAP METHOD

Year 2018, Volume: 1 Issue: 1, 1 - 5, 30.12.2018

Recep Bindak

Abstract

The
bootstrap method firstly was introduced by Efron [1] as a general method for assessing the statistical accuracy of an estimator.
Bootstrap is a computer-based re-sampling approach and a nonparametric
statistical inference method. In this study, the use of the Bootstrap method in
the parameter estimation of the linear regression is introduced and given a
sample application on a real data set. In addition, if the data set contains
outliers the effect that occurs in parameter estimation is examined. Confidence
intervals and standard errors have been identified for various bootstrap
repetitions numbers. As a result, it has been found that even 200 bootstrap
repetations may suffice to obtain proper results.

Keywords

Bootstrap method Resampling Linear regression Parameter estimation

References

  • [1]. Efron B. 1979, Bootstrap methods: Another look at the Jackknife. Annals of Statistics, 7: p. 1-26.
  • [2]. Kantar, Y.M., I. Usta, and Ş. Acıtaş, 2011. A Monte Carlo simulation study on partially adaptive estimators of linear regression models. Journal of Applied Statistics, 38(8): p. 1681-1699.
  • [3]. Efron, B., and R. Tibshirani, 1986. Bootstrap Methods for standat errors, confidence intervals and other measures of statistical accuracy. Statistical Science, 1: p. 54-77.
  • [4]. Sprenger, J, 2011. Science without (parametric) models: the case of bootstrap resampling. Synthese, 180: p. 65–76.
  • [5]. Takma, Ç., and H. Atıl, 2016. Study on bootstrap method and it’s application II confidence interval, hypothesis testing and regression analysis with bootstrap method [Bootstrap metodu ve uygulanışı üzerine bir çalışma 2. Güven aralıkları, hipotez testi ve regresyon analizinde bootstrap metodu]. Ege Üniversitesi Ziraat Fakültesi Dergisi, 43(2): p. 63-72.
  • [6]. Singh, K., and M. Xie, Bootstrap: A statistical method. In P. Peterson, E. Baker & B. McGaw (Eds.), International encyclopedia of education (3rd ed). 2010, Elsevier Science: Rutgers University- NJ, p. 46 –51.
  • [7]. Kreiss, J.P., and E. Paparoditis, 2011. Bootstrap methods for dependent data: A review. Journal of the Korean Statistical Society 40: p. 357–378.
  • [8]. Gonzàlez-Manteiga, W., and A. Martinez-Calvo, 2011. Botstrap in functional linear regression. Journal of Statistical Planning and Inference, 141: p. 453–461. doi:10.1016/j.jspi.2010.06.027
  • [9]. McMurry, T., and D.N. Politis, 2008. Bootstrap confidence intervals in nonparametric regression with built-in bias correction. Statistics and Probability Letters, 78: p. 2463–2469.
  • [10]. Buchholz, A., N. Holländer, and W. Sauerbrei, 2008. On properties of predictors derived with a two-step bootstrap model averaging approach-A simulation study in the linear regression model. Computational Statistics & Data Analysis, 52: p. 2778 – 2793.
  • [11]. Okutan, D., The usage of the Bootstrap method in regression analysis and its comparison with other methods. 2009, Ms Thesis Ege University: İzmir.
  • [12]. Amiri, S., and S. Zwanzig, 2011. Assessing the coefficient of variations of chemical data using bootstrap method. Journal of Chemometrics, 25(6): p. 295-300.
  • [13]. Amiri, S., and D. von Rosen, 2011. On the efficiency of bootstrap method into the analysis contingency table. Computer Methods and Programs in Biomedicine, 104(2): p. 182-187.
  • [14]. Baydılı, K.N., and D. Sığırlı, 2017. Comparison of variance homogenity tests for different distributions. Turkiye Klinikleri Journal of Biostatics, 9, doi: 10.5336/biostatic.2017-5631
  • [15]. Özdemir, A. F., and G. Navruz, 2016. The effect of number of bootstrap samples, trimming proportion and distribution to the results in bootstrap-t and percentile bootstrap methods [Bootstrap-t ve yüzdelik bootstrap yöntemlerinde tekrar sayısı, budama yüzdesi ve dağılımın sonuçlara etkisi]. Nevşehir Bilim ve Teknoloji Dergisi, 5(2): p. 74-85.
  • [16]. 16.Amiri, S., and R. Modaress, 2017. Comparison of tests of contingency tables. Journal of Biopharmaceutıcal Statıstics, http://dx.doi.org/10.1080/10543406.2016.1269786
  • [17]. Martin, M. A., and S. Roberts, 2010. Jackknife-after-bootstrapregression influence diagnostics. Journal of Nonparametric Statistics, 22(2): p. 257-269.
  • [18]. Beyaztas, U., A. Alin, and M.A. Martin, 2014. Robust BCa–JaB method as a diagnostic tool for linear regression models. Journal of Applied Statistics, 41(7): p. 1593-1610.
  • [19]. Beyaztas U, & Alin A. (2014) Jackknife-after-Bootstrap as logistic regression diagnostic tool. Communications in Statistics - Simulation and Computation, 43:9, 2047-2060.
  • [20]. Karlis D. 2004, An introduction to Bootstrap Methods. 17th Conference of Greek Statistical Society. http://stat-athens.aueb.gr/~karlis/lefkada/boot.pdf
  • [21]. Efron, B., and R. Tibshirani, An Introduction toThe Bootstrap. 1993: Chapman&Hall.Inc. USA,p. 87-107.

Year 2018, Volume: 1 Issue: 1, 1 - 5, 30.12.2018

Recep Bindak

Abstract

References

  • [1]. Efron B. 1979, Bootstrap methods: Another look at the Jackknife. Annals of Statistics, 7: p. 1-26.
  • [2]. Kantar, Y.M., I. Usta, and Ş. Acıtaş, 2011. A Monte Carlo simulation study on partially adaptive estimators of linear regression models. Journal of Applied Statistics, 38(8): p. 1681-1699.
  • [3]. Efron, B., and R. Tibshirani, 1986. Bootstrap Methods for standat errors, confidence intervals and other measures of statistical accuracy. Statistical Science, 1: p. 54-77.
  • [4]. Sprenger, J, 2011. Science without (parametric) models: the case of bootstrap resampling. Synthese, 180: p. 65–76.
  • [5]. Takma, Ç., and H. Atıl, 2016. Study on bootstrap method and it’s application II confidence interval, hypothesis testing and regression analysis with bootstrap method [Bootstrap metodu ve uygulanışı üzerine bir çalışma 2. Güven aralıkları, hipotez testi ve regresyon analizinde bootstrap metodu]. Ege Üniversitesi Ziraat Fakültesi Dergisi, 43(2): p. 63-72.
  • [6]. Singh, K., and M. Xie, Bootstrap: A statistical method. In P. Peterson, E. Baker & B. McGaw (Eds.), International encyclopedia of education (3rd ed). 2010, Elsevier Science: Rutgers University- NJ, p. 46 –51.
  • [7]. Kreiss, J.P., and E. Paparoditis, 2011. Bootstrap methods for dependent data: A review. Journal of the Korean Statistical Society 40: p. 357–378.
  • [8]. Gonzàlez-Manteiga, W., and A. Martinez-Calvo, 2011. Botstrap in functional linear regression. Journal of Statistical Planning and Inference, 141: p. 453–461. doi:10.1016/j.jspi.2010.06.027
  • [9]. McMurry, T., and D.N. Politis, 2008. Bootstrap confidence intervals in nonparametric regression with built-in bias correction. Statistics and Probability Letters, 78: p. 2463–2469.
  • [10]. Buchholz, A., N. Holländer, and W. Sauerbrei, 2008. On properties of predictors derived with a two-step bootstrap model averaging approach-A simulation study in the linear regression model. Computational Statistics & Data Analysis, 52: p. 2778 – 2793.
  • [11]. Okutan, D., The usage of the Bootstrap method in regression analysis and its comparison with other methods. 2009, Ms Thesis Ege University: İzmir.
  • [12]. Amiri, S., and S. Zwanzig, 2011. Assessing the coefficient of variations of chemical data using bootstrap method. Journal of Chemometrics, 25(6): p. 295-300.
  • [13]. Amiri, S., and D. von Rosen, 2011. On the efficiency of bootstrap method into the analysis contingency table. Computer Methods and Programs in Biomedicine, 104(2): p. 182-187.
  • [14]. Baydılı, K.N., and D. Sığırlı, 2017. Comparison of variance homogenity tests for different distributions. Turkiye Klinikleri Journal of Biostatics, 9, doi: 10.5336/biostatic.2017-5631
  • [15]. Özdemir, A. F., and G. Navruz, 2016. The effect of number of bootstrap samples, trimming proportion and distribution to the results in bootstrap-t and percentile bootstrap methods [Bootstrap-t ve yüzdelik bootstrap yöntemlerinde tekrar sayısı, budama yüzdesi ve dağılımın sonuçlara etkisi]. Nevşehir Bilim ve Teknoloji Dergisi, 5(2): p. 74-85.
  • [16]. 16.Amiri, S., and R. Modaress, 2017. Comparison of tests of contingency tables. Journal of Biopharmaceutıcal Statıstics, http://dx.doi.org/10.1080/10543406.2016.1269786
  • [17]. Martin, M. A., and S. Roberts, 2010. Jackknife-after-bootstrapregression influence diagnostics. Journal of Nonparametric Statistics, 22(2): p. 257-269.
  • [18]. Beyaztas, U., A. Alin, and M.A. Martin, 2014. Robust BCa–JaB method as a diagnostic tool for linear regression models. Journal of Applied Statistics, 41(7): p. 1593-1610.
  • [19]. Beyaztas U, & Alin A. (2014) Jackknife-after-Bootstrap as logistic regression diagnostic tool. Communications in Statistics - Simulation and Computation, 43:9, 2047-2060.
  • [20]. Karlis D. 2004, An introduction to Bootstrap Methods. 17th Conference of Greek Statistical Society. http://stat-athens.aueb.gr/~karlis/lefkada/boot.pdf
  • [21]. Efron, B., and R. Tibshirani, An Introduction toThe Bootstrap. 1993: Chapman&Hall.Inc. USA,p. 87-107.
There are 21 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Recep Bindak 0000-0002-0005-7862

Publication Date December 30, 2018
Acceptance Date July 26, 2018
Published in Issue Year 2018 Volume: 1 Issue: 1

Cite

APA Bindak, R. (2018). PARAMETER ESTIMATION FOR LINEAR REGRESSION USING BOOTSTRAP METHOD. The International Journal of Materials and Engineering Technology, 1(1), 1-5.
AMA Bindak R. PARAMETER ESTIMATION FOR LINEAR REGRESSION USING BOOTSTRAP METHOD. TIJMET. December 2018;1(1):1-5.
Chicago Bindak, Recep. “PARAMETER ESTIMATION FOR LINEAR REGRESSION USING BOOTSTRAP METHOD”. The International Journal of Materials and Engineering Technology 1, no. 1 (December 2018): 1-5.
EndNote Bindak R (December 1, 2018) PARAMETER ESTIMATION FOR LINEAR REGRESSION USING BOOTSTRAP METHOD. The International Journal of Materials and Engineering Technology 1 1 1–5.
IEEE R. Bindak, “PARAMETER ESTIMATION FOR LINEAR REGRESSION USING BOOTSTRAP METHOD”, TIJMET, vol. 1, no. 1, pp. 1–5, 2018.
ISNAD Bindak, Recep. “PARAMETER ESTIMATION FOR LINEAR REGRESSION USING BOOTSTRAP METHOD”. The International Journal of Materials and Engineering Technology 1/1 (December 2018), 1-5.
JAMA Bindak R. PARAMETER ESTIMATION FOR LINEAR REGRESSION USING BOOTSTRAP METHOD. TIJMET. 2018;1:1–5.
MLA Bindak, Recep. “PARAMETER ESTIMATION FOR LINEAR REGRESSION USING BOOTSTRAP METHOD”. The International Journal of Materials and Engineering Technology, vol. 1, no. 1, 2018, pp. 1-5.
Vancouver Bindak R. PARAMETER ESTIMATION FOR LINEAR REGRESSION USING BOOTSTRAP METHOD. TIJMET. 2018;1(1):1-5.
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