Research Article
Year 2021,
Volume: 6 Issue: 1, 15 - 26, 30.06.2021
Abstract
References
- Adichie, J.N. (1967). Estimates of Regression Parameters Based on Rank Tests. Annals of Mathematical Statistics, 38, p. 894-904.
- Akritas, M.G., Murphy, S.A., & LaValley, M.P. (1995). The Theil–Sen estimator with doubly censored data and applications to astronomy. J. Amer. Statist. Assoc. 90, 170–177.
- Birkes, D. & Dodge, Y. (1993) Alternative Methods of Regression. John Wiley & Sons Inc., NY, USA.
- Dang, X., Peng, H., Wang, X. & Zhang, H. (2008). Theil-Sen Estimators in a Multiple Linear Regression Model, Olemiss Edu, 2008.
- Erilli, N.A. & Alakuş, K. (2016). Parameter Estimation In Theil-Sen Regression Analysis With Jackknife Method. Eurasian Econometrics, Statistics & Empirical Economics Journal, v.5, p:28-41.
- 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.
- Gujarati, D.N. (2002). Basic Econometrics. McGraw Hill pub., NY, USA.
- Hanxiang, P., Shaoli W. & Xueqin, W. (2008). Consistency and asymptotic distribution of the Theil–Sen estimator. Journal of Statistical Planning and Inference, 138, 1836 – 1850.
- Hodges, J. L. & Lehmann, E.L., (1963). Estimates of location based on rank tests. Ann. Math. Statist. 34, 598–611.
- Lavagnini, I., Badocco, D., Pastore, P. & Magno, F. (2011). Theil–Sen nonparametric regression technique on univariate calibration, inverse regression and detection limits. Talanta, 87, p.180-188.
- Lehmann, E.L., & Dabrera H.J.M. (1975). Nonparametrics: Statistical Methods Based on Ranks. SF, USA: Holden-Day Inc. pp 304. Sen, P.K. (1968). Estimates of the regression coefficient based on Kendall's tau. Journal of the American Statistical Association, 63: 1379–1389.
- Spath, H. (1992). Mathematical Algorithms for Linear Regression. London: Academic Press, pp 304.
- Sprent, P. (1989). Applied Nonparametric Statistical Methods. Chapman and Hall Pub., London, UK.
- Theil, H. (1950) A-Rank Invariant Method of Linear and Polynomial Regression Analysis. III. Nederl. Akad. Wetensch.Proc., Series A, 53, 1397‐1412.
- Tukey, J.W. (1977). Exploratory Data Analysis. Reading, MA: Addison-Wesley, pp. 46-47, 1977.
- Wang, X.Q. (2005). Asymptotics of the Theil–Sen estimator in simple linear regression models with a random covariate. Nonparametric Statist. 17, 107–120.
- Wilcox, R.R. (1998). Simulations on the Theil-Sen regression estimator with right-censored data. Statistics & Probability Letters, 39, 43-47.
Year 2021,
Volume: 6 Issue: 1, 15 - 26, 30.06.2021
Abstract
Theil-Sen regression analysis is the most preferred method in non-parametric regression analysis. In the Theil-Sen method, calculations are made with the median parameter. In this study, it was proposed to calculate the trimean parameter instead of the median parameter. In this way, the effects of the outliers in the data on the model are fully reflected. In applications of one real-life and two simulation data, the results obtained with the use of trimean were more successful. It is recommended to use the trimean parameter instead of the median parameter in data structures with an excess of outliers.
References
- Adichie, J.N. (1967). Estimates of Regression Parameters Based on Rank Tests. Annals of Mathematical Statistics, 38, p. 894-904.
- Akritas, M.G., Murphy, S.A., & LaValley, M.P. (1995). The Theil–Sen estimator with doubly censored data and applications to astronomy. J. Amer. Statist. Assoc. 90, 170–177.
- Birkes, D. & Dodge, Y. (1993) Alternative Methods of Regression. John Wiley & Sons Inc., NY, USA.
- Dang, X., Peng, H., Wang, X. & Zhang, H. (2008). Theil-Sen Estimators in a Multiple Linear Regression Model, Olemiss Edu, 2008.
- Erilli, N.A. & Alakuş, K. (2016). Parameter Estimation In Theil-Sen Regression Analysis With Jackknife Method. Eurasian Econometrics, Statistics & Empirical Economics Journal, v.5, p:28-41.
- 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.
- Gujarati, D.N. (2002). Basic Econometrics. McGraw Hill pub., NY, USA.
- Hanxiang, P., Shaoli W. & Xueqin, W. (2008). Consistency and asymptotic distribution of the Theil–Sen estimator. Journal of Statistical Planning and Inference, 138, 1836 – 1850.
- Hodges, J. L. & Lehmann, E.L., (1963). Estimates of location based on rank tests. Ann. Math. Statist. 34, 598–611.
- Lavagnini, I., Badocco, D., Pastore, P. & Magno, F. (2011). Theil–Sen nonparametric regression technique on univariate calibration, inverse regression and detection limits. Talanta, 87, p.180-188.
- Lehmann, E.L., & Dabrera H.J.M. (1975). Nonparametrics: Statistical Methods Based on Ranks. SF, USA: Holden-Day Inc. pp 304. Sen, P.K. (1968). Estimates of the regression coefficient based on Kendall's tau. Journal of the American Statistical Association, 63: 1379–1389.
- Spath, H. (1992). Mathematical Algorithms for Linear Regression. London: Academic Press, pp 304.
- Sprent, P. (1989). Applied Nonparametric Statistical Methods. Chapman and Hall Pub., London, UK.
- Theil, H. (1950) A-Rank Invariant Method of Linear and Polynomial Regression Analysis. III. Nederl. Akad. Wetensch.Proc., Series A, 53, 1397‐1412.
- Tukey, J.W. (1977). Exploratory Data Analysis. Reading, MA: Addison-Wesley, pp. 46-47, 1977.
- Wang, X.Q. (2005). Asymptotics of the Theil–Sen estimator in simple linear regression models with a random covariate. Nonparametric Statist. 17, 107–120.
- Wilcox, R.R. (1998). Simulations on the Theil-Sen regression estimator with right-censored data. Statistics & Probability Letters, 39, 43-47.
There are 17 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Business Administration |
| Journal Section | Articles |
| Authors | |
| Publication Date | June 30, 2021 |
| Submission Date | November 17, 2020 |
| Acceptance Date | January 19, 2021 |
| Published in Issue | Year 2021 Volume: 6 Issue: 1 |
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