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Journals / Alphanumeric Journal / 2021 / Cilt: 9 - Sayı: 2

Contributions to Theil-Sen Regression Analysis Parameter Estimation with Weighted Median

Cem ÖZTAŞ
Necati Alp ERİLLİ
Pages
259–268
Publication Date
2022-10-11
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

It has been seen that the obtained results are successful compared to the classical Theil-Sen results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Regression analysis is one of the most commonly used estimation methods.
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Key Findings & Data:In statistical studies, some assumptions must be fully met to make good estimations with regression analysis.
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Conclusion & Impact:It has been seen that the obtained results are successful compared to the classical Theil-Sen results.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

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.

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Cite This Article

ÖZTAŞ, C., ERİLLİ, N. A. (2022). Contributions to Theil-Sen Regression Analysis Parameter Estimation with Weighted Median. Alphanumeric Journal, Cilt: 9 - Sayı: 2, 259–268. https://ajindex.com/articles/435094

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References (8)

  1. Akritas, M.G., Murphy, S.A., LaValley, M.P. (1995). J. Am. Stat. Assoc., 90, 170. Alakuş K, Erilli N.A. (2014). Non‐Parametric Regression Estimation for Data with Equal Value, European Scientific Journal (ESJ),2014, 4, 1857‐ 7431. Birkes D., Dodge Y. (1993). Alternative Methods of Regression. John Wiley and Sons Inc., NY. USA. Bowerman, B.L., O’Connell, R.T., Murphree, E.S., Orris, J.B. (2013). İşletme İstatistiğinin Temelleri. Çeviri editörleri: Neyran Orhunbilge, Mustafa Can, Şebnem Er. Nobel yayınları, Ankara.
  2. Erilli, N.A., Alakuş, K. (2016). Parameter Estimation In Theil-Sen regression analysis with Jackknife method. Eurasian Econometrics, Statistics & Empirical Economics Journal, 5, 28-41.
  3. Erilli, N.A. (2015). İstatistik-2. Seçkin Yayıncılık, Ankara.
  4. 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), 3, 303‐316. Gujarati, D. (1999). Temel Ekonometri. Çevirenler: Ümit Şenesen, G. Günlük Şenesen. Literatür Yayıncılık, İstanbul.
  5. 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., Sprent, P. (1983). Non-Parametric Regression. Journal of The Royal Statistical Society. Ser., A., 146, 182-191.
  6. Lavagnini, I., Badocco, D., Pastore, P., Magno, F. (2011). Theil‐Sen nonpara‐metric 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.
  7. 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.
  8. 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, 138:6, Pages 1660‐1678. Wilcox, R. (1998). A note on the Theil-Sen regression estimator wh