Doğrusal Regresyon Modelinde Parametrik ve Parametrik Olmayan Tahmin Yöntemlerinin Karşılaştırması

Bu çalışmada, basit doğrusal regresyon modelinde parametrik ve parametrik olmayan analiz yöntemlerinin karşılaştırmalı olarak incelenmesi amaçlanmıştır. Modelin parametrik analizinde EKK tahmini, parametrik olmayan analizinde ise medyana göre parametre tahmini yapan Mood-Brown ve Theil-Sen yöntemleri tanıtılmıştır. Ayrıca Theil-Sen yöntemine ait çeşitli ağırlıklar incelenerek parametre tahmin ediciler tartışılmıştır. Parametrik olmayan yöntemlere olan ihtiyacı göstermek amacı ile sonuçlar gerçek yaşam verisi üzerinde değerlendirilmiştir.

Anahtar Kelimeler:

Aykırı Değer, EKK, Mood-Brown Tahmini, Theil-Sen Tahmini, Ortalama Mutlak Sapma, Medyan

Comparison of Parametric and Non-Parametric Estimation Methods in Linear Regression Model

In this study, the aim was to review the methods of parametric and non-parametric analyses in simple linear regression model. The least squares estimator (LSE) in parametric analysis of the model, and Mood-Brown and Theil-Sen methods that estimates the parameters according to the median value in non-parametric analysis of the model are introduced. Also, various weights of Theil-Sen method are examined and estimators are discussed. In an attempt to show the need for non-parametric methods, results are evaluated based on real life data.

Keywords:

Outlier, Least Squares, Non-Parametric Estimation Methods, Median, Mean Absolute Deviation,

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Brown, G. W., & Mood, A. M. (1951). On median tests for linear hypotheses. In Proceedings of the Second Berkeley Symposium on Mathematical Statistics and Probability. The Regents of the University of California.
Candan, M. (1995). Robust estimators in linear regression analysis. Master Thesis. Hacettepe University. Graduate School of Sciences, Ankara, 47096.
D’Abrera, H. J. M., & Lehmann, E. L. (1975). Nonparametrics: statistical methods based on ranks. Holden-Day.
Daniel, C., & Wood, F. S. (1980). Fitting equations to data: computer analysis of multifactor data. John Wiley & Sons, Inc..
Daniel, W. W. (1990). Applied Nonparametric Statistics, 2nd. Brooks/Cole.
Hussain, S. S., & Sprent, P. (1983). Non‐parametric regression. Journal of the Royal Statistical Society: Series A (General), 146(2), 182-191.
Kıroğlu, G. (2001). Applied Nonparametric Statistical Methods. Mimar Sinan University Faculty of Art and Sciences, Istanbul.
Maritz, J. S. (1979). On Theil’s method in distribution‐free regression. Australian Journal of Statistics, 21(1), 30-35.
Mood, A. M., & Graybill, F. A. (1950). Introduction to the Theory of Statistics, New York: Mc-Graw-IIill Book Co.
Randles, R. H., & Wolfe, D. A. (1979). Introduction to the theory of nonparametric statistics. New York: John Willey & Sons.
Rao, K. M., & Gore, A. P. (1982). Nonparametric tests for intercept in linear regression problems. Australian Journal of Statistics, 24(1), 42-50.
Scholz, F. W. (1978). Weighted median regression estimates. The Annals of Statistics, 603-609.
Sen, P. K. (1968). Estimates of the regression coefficient based on Kendall’s tau. Journal of the American statistical association, 63(324), 1379-1389.
Sievers, G. L. (1978). Weighted rank statistics for simple linear regression. Journal of the American Statistical Association, 73(363), 628-631.
Theil, H. (1950). A rank-invariant method of linear and polynomial regression analysis, Part 3. In Proceedings of Koninalijke Nederlandse Akademie van Weinenschatpen A (Vol. 53, pp. 1397- 1412).
Toka, O., Çetin M. & Altunay, S. A. (2011). Comparison of Robust and Theil Estimators in Simple Linear Regression. TUIK, Statistics Research Journal. Volume: 08. Issue: 03. Category: Page: 45-53. ISSN No. 1303-6319.
Wang, X., & Yu, Q. (2005). Unbiasedness of the Theil–Sen estimator. Nonparametric Statistics, 17(6), 685-695.
Yıldız, N. & Topal M., (2001). Investigation of Nonparametric Regression Methods. Atatürk University, Faculty of Agriculture Journal, 32(4), 429-435.
Zaman, T. (2017). Contributions to the jackknife estimation and test problems in multiple linear regression analysis. Doctoral Thesis. Ondokuz Mayıs University. Graduate School of Sciences. Samsun 468099.
Zaman, T., & Alakuş, K. (2016). Some Robust Estimation Methods and Their Applications. Alphanumeric Journal, 3(2), 73-82.