Kantil Regresyon

Year 2017, Volume: 9 Issue: 2, 137 - 146, 15.06.2017

Arzu Altın Yavuz Ebru Gündoğan Aşık

https://doi.org/10.29137/umagd.352530

Cited By: 13

Abstract

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.

Keywords

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

Quantile Regression

Abstract

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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