Some Robust Estimation Methods and Their Applications

Abstract

This study examines robust regression methods which are used for the solution of problems caused by the situations in which the assumptions of LSM technique, which is commonly used for the prediction of linear regression models, cannot be used. Robust estimators are not influenced by small deviations and discrepancies. For this purpose, some robust regression techniques which are used in situations in which the assumptions cannot be made were introduced and parameter estimation algorithms of these techniques were analyzed. Regression models of the methods of Lad, Weighted –M regression, Theil regression and Least Median Squares, coefficients of determination and average absolute deviations were calculated and the results were discussed as to which of these methods gave better results. This study examines robust regression methods which are used for the solution of problems caused by the situations in which the assumptions of LSM technique, which is commonly used for the prediction of linear regression models, cannot be used. Robust estimators are not influenced by small deviations and discrepancies. For this purpose, some robust regression techniques which are used in situations in which the assumptions cannot be made were introduced and parameter estimation algorithms of these techniques were analyzed. Regression models of the methods of Lad, Weighted –M regression, Theil regression and Least Median Squares, coefficients of determination and average absolute deviations were calculated and the results were discussed as to which of these methods gave better results.

Bazı Robust Tahmin Yöntemleri Ve Uygulamaları

Öz

Bu çalışmada doğrusal regresyon modellerinin tahmininde yaygın olarak kullanılan EKK tekniğinin varsayımlarının sağlanmamasından kaynaklanan problemlerin çözümü için kullanılan Robust regresyon yöntemleri incelenmiştir. Robust tahmin ediciler küçük sapmalardan, aykırılıklardan etkilenmezler. Bu amaçla, çalışmada varsayımların sağlanmadığı durumlarda kullanılan bazı robust regresyon teknikleri tanıtılmıştır ve bu tekniklere ait parametre tahmin algoritmaları incelenmiştir. Uygulamada Lad, Ağırlıklı –M regresyon, Theil regresyon ve En küçük Medyan Kareler yöntemlerine ait regresyon modeli, belirleme katsayıları ve ortalama mutlak sapmalar hesaplanmış olup, bu tahmin edicilerden hangisinin daha iyi sonuç verdiği tartışılmıştır.

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