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REGRESYON ANALİZİNDE KULLANILAN EN KÜÇÜK KARELER VE EN KÜÇÜK MEDYAN KARELER YÖNTEMLERİNİN KARŞILAŞTIRILMASI

THE COMPARISON OF LEAST SQUARES AND LEAST MEDIAN SQUARES ESTIMATION METHODS WHICH ARE USED IN LINEAR REGRESSION ANALYSIS

Journal Name:

  • Süleyman Demirel Üniversitesi Fen Dergisi

Publication Year:

  • 2008

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
Regression analysis is one of the most commonly used statistical techniques. Out of many possible regression techniques, the Least Squares Method (LSM) has been generally adopted because of tradition and ease of computation. In data analysis and trend modelling applications the least squares (LS) estimator is widely used and LS regression is, in most cases, the method of choice. However, the crucial fact that the LS estimator is very sensitive to outlying observations may lead to unreliable results in the regression estimates and, hence, to a misleading interpretation of the data. To remedy this problem, some statistical techniques have been developed that are not so easily affected by outliers. These are the robust methods, the results of which remain trustworthy even if a certain amount of data is outlier. One of them is the least median squares method which is using in statistical analysis. In this study, estimation of Least Square and Least Median Square has been given. LS and LMS methods are applied and compared on differrent sample that can be produced by simulation study. To find whether there isimportant difference between methods are compared their estimations
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Abstract (Original Language): 
İstatistiksel yöntemler içerisinde yer alan regresyon çözümlemesi en çok kullanılan yöntemlerden biridir. Olası birçok regresyon yöntemlerinin dışında, genellikle matematiksel hesaplamalardaki kolaylığından dolayı, En Küçük Kareler yöntemi (EKK) en uygun tahmin yöntemi olarak kullanılmaktadır. Veri analizi ve ekonometri uygulamalarında EKK kestiricileri yaygın olarak tercih edilmektedir. Bununla birlikte EKK kestiricileri sapan değerlere karşı oldukça hassas olduğundan, veri kümesinin sapan değerler içermesi durumunda veriler hakkında EKK kestiricileriyle yapılacak yorumlamalar geçersiz ve yanıltıcı olabilmektedir. Bu gibi durumlarda sapan değerler için önerilen güçlü regresyon yöntemlerini tercih etmek, sonuçların güvenirliliği açısından daha uygundur. İstatistiksel çözümlemelerde kullanılan bu güçlü yöntemlerden biri de En Küçük Medyan Kareler yöntemidir (EKMK). Bu çalışmada, benzetim yoluyla oluşturulan veri kümelerinden yararlanılarak basit doğrusal regresyon modeli için EKK ve EKMK yöntemlerinden elde edilen model kestirim değerleri ((30, (3j, <j2, R2) karşılaştırılmıştır.
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  • 2
219-229
  • Turkish

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