Ekonometride Güncel Yöntemler ve Uygulamalar

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DOI :10.26650/B/SS10.2021.013.11   IUP :10.26650/B/SS10.2021.013.11    Tam Metin (PDF)

Use of Weighted Median in THEIL-SEN Regression Analysis

Necati Alp Erilli

Regression analysis; is one of the most used analytical techniques in statistical prediction studies. The aim of regression analysis; to investigate the relationship between the dependent and independent variable or variables, which is estimated to have a cause-effect relationship between them, to explain the assumed relationship between variables functionally and to define this relationship with a model. Non-parametric regression analysis is a method used in cases where some assumptions that are valid for parametric regression methods cannot be met and give successful results. Nonparametric methods make calculations with the median parameter instead of arithmetic mean. The median parameter does not reflect the effect of outliers on the calculations. Weighted Median calculates the contribution of outlier values to the model even though it gives weight to each observation value. In this study, the Weighted Median parameter was used in the Theil-Sen method which is frequently used in nonparametric regression analysis. Optimum and Hodges-Lehmann calculations which are used in the computation of constant parameters in the Theil-Sen method are also used in this study. The results obtained from Theil-Sen, Hodges-Lehmann and Optimum method used with Weighted Median were tested in different data structures. Thus, the advantages or weaknesses of the use of the weighted median parameter in the Theil-Sen method over the classical methods were determined.


Anahtar Kelimeler: Theil-Sen Regression, Weighted Median, Non-parametric Regression Analysis, Hodges-Lehmann, Optimum

Referanslar

  • Bi rkes, D., & Dodge Y. (1993). Alternative Methods of Regression. NY, USA: John Wiley & Sons Inc. google scholar
  • Bo werman, B. L., O’Connell, R. T., Murphree, E. S., & Orris, J. B. (2013). İşletme İstatistiğinin Temelleri. (N. Orhunbilge, M. Can & Ş. Er, Çev.) Ankara: Nobel Yayınları. google scholar
  • Dang, X., Peng, H., Wang, X., & H. Zhang (2008). Theil-Sen Estimators in a Multiple Linear Regression Model, Submitted paper. Available on http://home.olemiss.edu/~xdang/papers. google scholar
  • Erilli, N. A. (2018). İstatistik-2. Ankara: Seçkin Yayınları. google scholar
  • Erilli, N. A., & Alakus K. (2014). Non-Parametric Regression Estimation for Data with Equal Values. European Scientific Journal, 10(4), 70-82. google scholar
  • Eubank, R. L. (1988). Spline Smoothing and Nonparametric regression. New York, USA: Marcel Dekker Inc. google scholar
  • Fernandes, R., & Leblanc, S. G. (2005). Parametric (modified least squares) and non-parametric (Theil-Sen) linear regressions for predicting biophysical parameters in the presence of measurement errors. Remote Sensing of Environment, 95, 303-316. google scholar
  • Gujarati, D. (1999). Temel Ekonometri. (Ü. Şenesen & G. Günlük Şenesen, Çev.) İstanbul: Literatür Yayıncılık. google scholar
  • Hardle, W. (1994). Applied Nonparametric Regression. London, UK: Cambridge University Press. google scholar
  • Hodges, J. L., & Lehmann, E. L. (1963). Estimates of location based on rank tests. Ann. Math. Statistics, 34, 598-611. google scholar
  • Horowitz, J. L. (1993). Semiparametric Estimation of a Work-Trip Mode Choice Model. Journal of Econometrics, 58, 49-70. google scholar
  • Lavagnini, I., Badocco, D., Pastore, P., & Magno F. (2011). Theil-Sen nonparametric regression technique on univariate calibration, inverse regression and detection limits. Talanta, 87, 180-188. google scholar
  • Lehmann, E. L., & Dabrera H. J. M. (1975). Nonparametrics: Statistical Methods Based on Ranks. SF, USA: Holden-Day Inc. google scholar
  • Peng, H., Wang, S., & Wang X. (2008). Consistency and asymptotic distribution of the Theil-Sen estimator. Journal ofStatistical Planning and Inference, 138, 1836-1850. google scholar
  • Scholz, F. W. (1978). Weighted median regression estimates. The annals of statistics, 6(3), 603-609. google scholar
  • Sen, P. K. (1968). Estimates of the regression coefficient based on Kendall’s tau. Journal of the American Statistical Association, 63, 1379-1389. google scholar
  • Siegel, A. F. (1982). Robust regression using repeated medians. Biometrika, 69(1), 242-244. google scholar
  • Takezawa, K. (2006). Introduction to Nonparametric Regression. Canada: Wiley-Interscience. google scholar
  • Theil, H. A. (1950). Rank invariant method of linear and polynomial regression analysis. III. Nederl.Akad. Wetensch.Proc., Series A, 53, 1397-1412. google scholar
  • Topal, M. (1999). Nonparametrik regresyon metodlarının incelenmesi (Yüksek lisans tezi, Atatürk Üniversitesi, Fen Bilimleri Enstitüsü, Erzurum). https://tez.yok.gov.tr/UlusalTezMerkezi/ adresinden edinilmiştir. google scholar
  • Wilcox, R. R. (1998). Simulations on the Theil-Sen regression estimator with right-censored data. Statistics & Probability Letters, 39, 43-47. google scholar
  • Zaman, T., & Alakus, K. (2019). Comparison of Parametric and Non-Parametric Estimation Methods in Linear Regression Model. alphanumeric journal, 7(1), 13-24. google scholar
  • Zhou, W., & Serfling, R. (2008). Multivariate spatial U-quantiles: A Bahadur-Kiefer representation, a Theil-Sen estimator for multiple regression, and a robust dispersion estimator. Journal of Statistical Planning and Inference, 138, 1660-1678. google scholar


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