Karma Denemelerde Sınırlı Etkili Regresyon Tahmin Edicileri

Karma denemelerde regresyon katsayılarını tahmin etmek amacıyla en sık kullanılan tahmin edici En küçük kareler tahmin edicisidir. Fakat bu tahmin edici çoklu bağlantı ve/veya sapan değer problemlerine karşı çok hassastır. Bu çalışmanın amacı karma modellerin regresyon parametrelerinin tahminlerini bahsi geçen problemlere karşı daha dirençli olacak biçimde tahmin edebilecek bir tahmin edici önermektir. Bunun için y ve/veya x yönündeki aykırı değerlere kaşı daha dirençli olan Genelleştirilmiş M (GM) tahmini ile çoklu bağlantı problemine karşı etkili olan ridge ve liu gibi yanlı regresyon tahmin edicileri birlikte kullanılmıştır. Önerilen tahmin edicinin hata kareler ortalaması (MSE) incelenerek bunun yanlı ve GM tahminlerinden daha küçük olduğu gösterilmiş ve performansı örneklerle gösterilmiştir.

Bounded-Influence Regression Estimation for Mixture Experiments

Ordinary Least Squares (OLS) estimator is widely used technique for estimating the regressioncoefficient in mixture experiments. But this estimator is very sensitive to outliers and/or multicollinearityproblems. The aim of this paper is to propose estimators for the regression parameters of a mixture modelthat can combat with the above problems. For this purpose, Generalized M (GM) estimation, which ismore resistant to outliers in the y and / or x directions and regression estimators such as ridge and Liu,which is effective against the multicollinearity, were used together. The Mean Square Error (MSE)properties of proposed estimator has been examined and shown to be smaller than biased and GMestimates. Also performance of the combined estimator is illustrated by examples.

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