TY  - JOUR
T1  - PARAMETER ESTIMATION FOR LINEAR REGRESSION USING BOOTSTRAP METHOD
AU  - Bindak, Recep
PY  - 2018
DA  - December
Y2  - 2018
JF  - The International Journal of Materials and Engineering Technology
JO  - TIJMET
PB  - Necip Fazıl YILMAZ
WT  - DergiPark
SN  - 2667-4033
SP  - 1
EP  - 5
VL  - 1
IS  - 1
LA  - en
AB  - Thebootstrap 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 nonparametricstatistical inference method. In this study, the use of the Bootstrap method inthe parameter estimation of the linear regression is introduced and given asample application on a real data set. In addition, if the data set containsoutliers the effect that occurs in parameter estimation is examined. Confidenceintervals and standard errors have been identified for various bootstraprepetitions numbers. As a result, it has been found that even 200 bootstraprepetations may suffice to obtain proper results.
KW  - Bootstrap method
KW  - Resampling
KW  - Linear regression
KW  - Parameter estimation
CR  - [1].  Efron B. 1979, Bootstrap methods: Another look at the Jackknife. Annals of Statistics, 7: p. 1-26.
CR  - [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.
CR  - [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.
CR  - [4]. Sprenger, J, 2011. Science without (parametric) models: the case of bootstrap resampling. Synthese, 180: p. 65–76.
CR  - [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.
CR  - [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.
CR  - [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.
CR  - [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
CR  - [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.
CR  - [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.
CR  - [11]. Okutan, D., The usage of the Bootstrap method in regression analysis and its comparison with other methods. 2009, Ms Thesis Ege University: İzmir.
CR  - [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.
CR  - [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.
CR  - [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
CR  - [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.
CR  - [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
CR  - [17]. Martin, M. A., and S. Roberts, 2010. Jackknife-after-bootstrapregression influence diagnostics. Journal of Nonparametric Statistics, 22(2): p. 257-269.
CR  - [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.
CR  - [19]. Beyaztas U, & Alin A. (2014) Jackknife-after-Bootstrap as logistic regression diagnostic tool. Communications in Statistics - Simulation and Computation, 43:9, 2047-2060.
CR  - [20]. Karlis D. 2004, An introduction to Bootstrap Methods. 17th Conference of Greek Statistical Society. http://stat-athens.aueb.gr/~karlis/lefkada/boot.pdf
CR  - [21]. Efron, B., and R. Tibshirani, An Introduction toThe Bootstrap. 1993: Chapman&Hall.Inc. USA,p. 87-107.
UR  - http://dergipark.org.tr/en/pub/tijmet/issue//420279
L1  - http://dergipark.org.tr/en/download/article-file/526601
ER  -