Some Regression Methods Based on Principal Components

Principal component analysis (PCA) is commonly used technique in data processing and dimensionality reduction. However, PCA is very sensitive to outliers. To deal with this problem, the robust principal component analysis (RPCA) using Projection-Pursuit (PP) is a very appealing method. On the other hand, combining PCA on explanatory variables with least squares regression yields to principal component regression (PCR). Taking into consideration this general structure of PCR, we combine (R)PCA with OLS and MM regression estimators and show the performances of examined methods on extensive simulation studies and real data examples.

Anahtar Kelimeler:

Ordinary Least Squares, Principal Component Analysis, Principal Component Regression, Robustness

Temel Bileşenlere Dayalı Bazı Regresyon Yöntemleri

Temel Bileşen Analizi (TBA) veri işleme ve boyut indirgeme için sıklıkla kullanılan bir tekniktir. Ancak, TBA verideki sapan değerlere karşı oldukça duyarlıdır. Bu problemle başa çıkmak için iz düşüm takibini (projection pursuit) temel alan dayanıklı TBA kullanımı oldukça dikkat çekici bir yöntem olarak ileri sürülmüştür. Diğer taraftan, Temel Bileşen Regresyonu (TBR), TBA ile en küçük kareler regresyonunun birleşimi olarak görülebilmektedir. Bu çalışmada, TBR’nin bu genel yapısı dikkate alınarak, sapan değerlere karşı dirençli olan versiyonları üzerinde çalışılmıştır. İncelenen yöntemlerin performans karşılaştırmaları detaylı bir benzetim çalışması ve çeşitli gerçek veri kümeleri üzerinde gösterilmiştir.

Keywords:

En Küçük Kareler, Temel Bileşen Analizi, Temel Bileşen Regresyonu,

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