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Journals / Uluslararası Sosyal Siyasal ve Mali Araştırmalar Dergisi / 2026 / Cilt: 6 Sayı: 2

Estimation of a Multiple Regression Model Involving Ill-Conditioning and Ill-Posedness Problems Using the Generalized Maximum Entropy Method

Genelleştirilmiş Maksimum Entropi Yöntemi ile Kötü Koşulluluk ve Eksik Sunumluluk Problemlerini İçeren Çoklu Regresyon Modeli Tahmini

Sümeyya Sayılkan(ÇUKUROVA ÜNİVERSİTESİ)0009-0006-0395-1030
Sibel Örk Özel(ÇUKUROVA ÜNİVERSİTESİ)0000-0002-7030-3512
Pages
244–259
Publication Date
2026-10-24
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The results show that the classical OLS approach is inadequate when multicollinearity is present.

📌 3 Key Takeaways

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Objective & Hypothesis:This study investigates the impact of econometric issues such as multicollinearity and underdetermination on regression analyses, and compares the performance of Ridge Regression and the Generalized Maximum Entropy (GME) method, both designed to address these challenges, using Mean Squared Error (MSE) as the evaluation criterion.
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Key Findings & Data:Agricultural input-output and GDP data for the United States from 1948 to 1988 were used to estimate two different models.
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Conclusion & Impact:The results show that the classical OLS approach is inadequate when multicollinearity is present.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:kötü koşulluluk · eksik sunumluluk · ridge tahmin edici

Abstract

This study investigates the impact of econometric issues such as multicollinearity and underdetermination on regression analyses, and compares the performance of Ridge Regression and the Generalized Maximum Entropy (GME) method, both designed to address these challenges, using Mean Squared Error (MSE) as the evaluation criterion. Agricultural input-output and GDP data for the United States from 1948 to 1988 were used to estimate two different models. Each model was analyzed using Ordinary Least Squares (OLS), Ridge Regression, and GME methods. The results show that the classical OLS approach is inadequate when multicollinearity is present. Ridge Regression provides more stable and balanced parameter estimates, while GME produces the lowest MSE values, particularly in underdetermined systems when sign constraints are applied. Since the study relies exclusively on existing U.S. datasets, the generalizability of the results to other countries or time periods is limited. Moreover, the performance of the methods is sensitive to the structure of the data and the choice of parameters. When evaluated in terms of MSE, the GME method emerges as a robust and effective alternative estimation approach, especially in situations involving underdetermined systems with appropriate constraints.

Özet

Bu çalışma, çoklu doğrusal bağlantı (multicollinearity) ve eksik belirlenmişlik (underdetermination) gibi ekonometrik sorunların regresyon analizleri üzerindeki etkisini incelemekte ve bu sorunları ele almak üzere geliştirilmiş Ridge Regresyonu ile Genelleştirilmiş Maksimum Entropi (GME) yöntemlerini, değerlendirme ölçütü olarak Ortalama Kare Hata (MSE) kullanarak karşılaştırmaktadır. 1948–1988 dönemine ait Amerika Birleşik Devletleri tarımsal girdi-çıktı ve GSYH verileri kullanılarak iki farklı model tahmin edilmiştir. Her bir model En Küçük Kareler (EKK/OLS), Ridge Regresyonu ve GME yöntemleriyle analiz edilmiştir. Elde edilen sonuçlar, çoklu doğrusal bağlantının var olduğu durumlarda klasik OLS yaklaşımının yetersiz kaldığını göstermektedir. Ridge Regresyonu daha istikrarlı ve dengeli parametre tahminleri sunarken, GME yöntemi özellikle işaret kısıtlarının uygulandığı eksik belirlenmiş sistemlerde en düşük MSE değerlerini üretmektedir. Çalışmanın yalnızca mevcut ABD verilerine dayanması, sonuçların diğer ülkelere veya dönemlere genellenebilirliğini sınırlamaktadır. Ayrıca yöntemlerin performansı, veri yapısına ve seçilen parametrelere duyarlıdır. MSE açısından değerlendirildiğinde, GME yöntemi özellikle uygun kısıtların bulunduğu eksik belirlenmiş sistemlerde sağlam ve etkili bir alternatif tahmin yaklaşımı olarak öne çıkmaktadır.

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Cite This Article

Sayılkan, S., Özel, S. Ö. (2026). Estimation of a Multiple Regression Model Involving Ill-Conditioning and Ill-Posedness Problems Using the Generalized Maximum Entropy Method. Uluslararası Sosyal Siyasal ve Mali Araştırmalar Dergisi, Cilt: 6 Sayı: 2, 244–259. https://doi.org/10.70101/ussmad.1904596

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