Ridge-Robust-Boosting Ensemble Regression Approach

Öz

In this study, two important problems frequently encountered in regression analysis, multicollinearity and the effects of outliers, are examined. Multicollinearity refers to the high level of correlation between independent variables in the regression model. This may make it difficult to estimate the coefficients and reduce the reliability of the estimated coefficients. Outliers may affect the general trend and mislead the results. The aim of this study is to develop a regression model that can address these two problems simultaneously. The proposed Ridge-Robust-Boosting Ensemble Regression model is designed to provide a solution to these problems. This model reduces multicollinearity using Ridge regression and thus stabilizes the correlation between independent variables. It also aims to be robust to outliers by using robust regression. In this way, it reduces the impact of rare but influential observations on forecasts. Moreover, it aims to improve the forecasting performance by using boosting methods. The simulation study conducted for the purpose of the study includes the evaluation of model performances by adding different multicollinearity levels and outlier ratios to a random data set consisting of 1000 observations. The results obtained show that the proposed Ridge-Robust-Boosting Ensemble Regression model outperforms other regression models in data sets with different multicollinearity levels and outlier rates. This suggests that the proposed model is a more reliable and flexible solution in general.

Anahtar Kelimeler

• Multicollinearity
• outlier
• Ridge-Robust-Boosting regression

Rigde-Robust-Boosting Topluluk Regresyon Yaklaşımı

Öz

Bu çalışmada, regresyon analizinde sıkça karşılaşılan iki önemli olan sorun, çoklu doğrusal bağlantı ve aykırı değerlerin etkileri incelenmiştir. Çoklu doğrusal bağlantı, regresyon modelindeki bağımsız değişkenler arasındaki yüksek düzeyde ilişkiyi ifade etmektedir. Bu durum, katsayıların tahmin edilmesini zorlaştırabilir ve tahmin edilen katsayıların güvenilirliğini azaltabilir. Aykırı değerler ise genel eğilimi etkileyebilir ve sonuçları yanıltabilir. Çalışmanın amacı, bu iki sorunu aynı anda ele alabilen bir regresyon modeli geliştirmektir. Önerilen Ridge-Robust-Boosting Topluluk Regresyon modeli, bu sorunlara çözüm sunmak üzere tasarlanmıştır. Bu model, Ridge regresyonunu kullanarak çoklu doğrusal bağlantıyı azaltmakta ve böylece bağımsız değişkenler arasındaki korelasyonu dengelemektedir. Ayrıca, Robust regresyonu kullanarak aykırı değerlere karşı dirençli olmayı hedeflemektedir. Bu sayede, nadir ancak etkili gözlemlerin tahminler üzerindeki etkisini azaltmaktadır. Ayrıca, Boosting yöntemlerini kullanarak tahmin performansını artırmayı hedeflemektedir. Çalışmanın amacı kapsamında yapılan simülasyon çalışması, 1000 gözlemden oluşan rastgele bir veri setine farklı çoklu doğrusallık ve aykırı değer eklenerek model performanslarının değerlendirilmesini içermektedir. Elde edilen sonuçlar, önerilen Ridge-Robust-Boosting Topluluk Regresyon modelinin, farklı çoklu doğrusallık düzeyleri ve aykırı değer oranlarına sahip veri setlerinde diğer regresyon modellerine göre daha üstün bir performans sergilediğini göstermektedir. Bu durum önerilen modelin genel olarak daha güvenilir ve esnek bir çözüm olduğunu ortaya koymaktadır.

Anahtar Kelimeler

• Çoklu doğrusal bağlantı
• aykırı değer
• Ridge-Robust-Boosting regresyon

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