Doğrusal Regresyonda Uç Değer Tespit Yöntemlerinin Karşılaştırılması: Çok Kriterli Karar Verme Yaklaşımı

Abstract

Bu makale, doğrusal regresyonda bilinen ve çağdaş aykırı değer tespit yöntemlerini değerlendirmek için bir dizi simülasyon çalışmasının uygulanmasına odaklanmaktadır. Bu simülasyonlar, gözlem sayılarının, parametre sayılarının ve kirlenmenin yönü ve oranı dahil olmak üzere farklı parametreler için gerçekleştirilmiştir. Kaydedilen nihai parametre tahminleri ve Çok Kriterli Karar Verme (ÇKKV) araçları kullanılarak tahmincilerin sıralanması sağlanmıştır. Çalışma, tahmincilerin başarısının simülasyon ayarlarına bağlı olarak değiştiğini ortaya koymaktadır. ÇKKV analizi sonuçları, kirlenme yönünün ve oranının bilinmediği durumlarda uygulanabilecek tahmincilerin sınırlı sayıda olduğunu göstermektedir. Ayrıca, en başarılı yöntemler artan hesaplama zamanı gerektirirken, bazı alternatifler orta sıralamalarla kısa süreler içinde uygulanabilirlik göstermektedir. Bu bulgular, altta yatan modelin bilindiği ve potansiyel aykırı değerlerin olabileceği senaryolarda regresyon analizi kullanan araştırmacılar için değerli öngörüler sunmaktadır.

Keywords

• uçdeğer teşhisi
• dayanıklı regresyon
• doğrusal regresyon
• karar analizi

Comparison of Outlier Detection Methods in Linear Regression: A Multiple-Criteria Decision-Making Approach

Abstract

This paper focuses on the application of a suite of simulation studies to assess wellknown and contemporary outlier detection methods in linear regression. These simulations vary across different parameters, including the number of observations, parameters, levels, and direction of contamination. The recorded final parameter estimates are used to rank the methods using Multiple-criteria decision-making (MCDM) tools. The study reveals that method success varies based on simulation settings. MCDM analysis results indicate a limited set of applicable methods when the contamination structure and level are unknown. Additionally, the most successful methods demand increased computation time, while some alternatives exhibit applicability within shorter durations with median rankings. These findings offer valuable insights for researchers employing regression analysis in scenarios where the underlying model is known, and the possibility of potential outliers exists.

Keywords

• outlier detection
• robust regression
• linear regression
• decision analysis

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