Kantil Regresyon

Regresyon analizi uygulama alanı en geniş olan istatistiksel analiz yöntemlerinden biridir. Birçok alanda tekniğinde olduğu gibi mühendislik alanında da yaygın olarak kullanılmaktadır. Regresyon analizinde kullanılan En Küçük Kareler (EKK) tekniğinin çıkarsama amaçlı kullanılabilmesi bazı varsayımların sağlanmasını zorunlu kılar. EKK tekniğinde hata terimleri dağılımının normal dağılıma sahip olmaması ve modelin aykırı değerler içermesi durumunda EKK tahmin edicileri etkinlik özelliklerini kaybetmektedir. Bu durumda alternatif regresyon tekniklerine başvurulmaktadır. Alternatif regresyon yöntemlerinden biri olan Kantil regresyon, klasik regresyon yöntemlerinin bazı sınırlamalarının üstesinden gelmektedir. Bu çalışmada Kantil regresyon yöntemi tanıtılmış ve bir mühendislik uygulaması üzerinde EKK tahmin edicileri ile karşılaştırılmıştır. Beton kırma deneyi için elde edilen sonuçlara göre, EKK yöntemi ile elde edilen modelin çıkarsama amaçlı kullanılamayacağı tespit edilmiştir. Bu durumda τ =0.75’inci ve τ =0.25’inci kantil değerine göre kurulan regresyon denklemi çıkarsama amaçlı kullanılabilir.

Anahtar Kelimeler:

Aykırı değer, Regresyon analizi, En Küçük Kareler, Kantil regresyon

Quantile Regression

Regression analysis is one of the most widely used statistical analysis methods. It is widely used in the engineering field as it is in many areas. The fact that the Least Squares (LS) technique used in regression analysis can be used for inference makes it necessary to provide some assumptions. In the LS, if the distribution of error terms does not have normal distribution and if the model contains outliers, the least squares estimators lose their efficiency properties. In this case, alternative regression techniques are applied. Quantile regression, one of the alternative regression methods, comes from overcoming some of the limitations of classical regression methods. In this study, the method of quantile regression is introduced and on an engineering application is compared with the estimators of the LS. According to the results obtained for the concrete breaking test, it has been determined that the model obtained by the method of LS can not be used for inference. İn this case, it can be used for inference the regression equation established for τ = 0.75th and τ = 0.25th quantile value.

Keywords:

Outlier, Regression analysis, Least Squares, Quantile regression,

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