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The Journal of Operations Research, Statistics, Econometrics and Management Information Systems
Contributions to Theil-Sen Regression Analysis Parameter Estimation with Weighted Median
Abstract
Regression analysis is one of the most commonly used estimation methods. In statistical studies, some assumptions must be fully met to make good estimations with regression analysis. Some of these assumptions are not always fulfilled in real life data. For such cases, alternative methods are used. One of them is Theil-sen method, which is one of the non-parametric regression analysis techniques. In this study, different analysis techniques were proposed by using the weighted median parameter instead of the median parameter used in the Theil-Sen regression method. With the proposed four different algorithms, new approaches to Theil-Sen regression analysis estimation have been introduced. It has been seen that the obtained results are successful compared to the classical Theil-Sen results.
Keywords: Mean Absolute Error, Non-Parametric Regression, Theil-Sen Method, Weighted Median
Jel Classification: C46
Suggested citation
Öztaş, C., Erilli, NA. (2021). Contributions to Theil-Sen Regression Analysis Parameter Estimation with Weighted Median. Alphanumeric Journal, 9(2), 259-268. http://dx.doi.org/10.17093/alphanumeric.998384
References
- Akritas, M.G., Murphy, S.A. and LaValley, M.P. (1995). The Theil–Sen estimator with doubly censored data and applications to astronomy. J. Am. Stat. Assoc., 90, 170.
- Alakuş, K., and Erilli, N.A. (2014). Non‐Parametric Regression Estimation for Data with Equal Value, European Scientific Journal (ESJ) ,2014, 4, 1857‐ 7431.
- Birkes, D. and Dodge, Y. (1993). Alternative Methods of Regression. John Wiley and Sons Inc., NY. USA.
- Bowerman, B.L., O’Connell, R.T., Murphree, E.S. and Orris, J.B. (2015). Essentials of Business Statistics, 5th edition. McGraw and Hill pub. USA.
- Erilli, N.A. and Alakuş, K. (2016). Parameter Estimation In Theil-Sen regression analysis with Jackknife method. Eurasian Econometrics, Statistics & Empirical Economics Journal, 5, 28-41.
- Erilli, N.A. (2015). İstatistik-2. Seçkin Pub., Ankara.
- Fernandes, R. and 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), 3, 303‐316.
- Gujarati, D. (1999). Temel Ekonometri. Translate: Ümit Şenesen, G. Günlük Şenesen. Literatür Pub., İstanbul.
- Hardle, W. (1994). Applied Nonparametric Regression. Cambridge University, UK.
- Horowitz, J.L. (1993). Semiparametric Estimation of a Work‐Trip Mode Choice Model, Journal of Econometrics, 58, 49‐70.
- Hussain, S.S. and Sprent, P. (1983). Non-Parametric Regression. Journal of The Royal Statistical Society. Ser., A., 146, 182-191.
- Lavagnini, I., Badocco, D., Pastore, P. and Magno, F. (2011). Theil‐Sen nonparametric regression technique on univariate calibration, inverse regression and detection limits, Talanta, Volume 87, Pages 180‐188.
- Sen, P.K. (1968). Estimates of The Regression Coefficient Based on Kendall’s Tau. J. Amer. Statist. Ass., 63, 1379-1389.
- Shen, G. (2009). Asymptotics of a Theil‐Sen‐type estimate in multiple linear regression
- Statistics & Probability Letters, volume 79, Issue 8, pp. 1053‐1064.
- Takezawa, K. (2006). Introduction to Nonparametric Regression. Wiley‐Interscience, Canada.
- Theil, H. (1950). A Rank Invariant Method of Linear and Polynomial Regression Analysis. III. Nederl. Akad. Wetensch. Proc., Series A, 53, 1397-1412.
- Zhou, W. and 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, 138:6, Pages 1660‐1678.
- Wilcox, R. (1998). A note on the Theil-Sen regression estimator when the regressor is random and the error term is heteroscedastic. Biometrical J. 40, 261–268.
2021.09.02.STAT.03
alphanumeric journal
Pages 259-268
Received: Sept. 21, 2021
Accepted: Nov. 22, 2021
Published: Dec. 31, 2021
2021 Öztaş, C., Erilli, NA.
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