Farklı Yanlılık Parametreleri İçin Ridge GM Tahmin Edicilerinin Performanslarının Karşılaştırılması

Yıl 2021, , 203 - 216, 30.06.2021

Melike Işılar , Y. Murat Bulut

https://doi.org/10.35193/bseufbd.877176

Cited By: 2

Öz

Çoklu lineer regresyon modelinde yaygın olarak karşılaşılan problemler çoklu iç ilişki ve aykırı değer problemleridir. Bu iki problemin eş anlı çözümleri için literatürde sağlam yanlı tahmin ediciler üzerine pek çok çalışma mevcuttur. Bu tahmin edicilerden en yaygın kullanılanları sağlam Ridge tahmin edicileridir. Yanlılık parametresine bağlı olan Ridge tahmin edicisine ilişkin günümüzde de pek çok çalışma yapılmaktadır. Yapılan çalışmalarda yanlılık parametresinin performansı klasik Ridge tahmin edicisinde incelenmektedir. Bu çalışmada her iki değişkende de aykırı değer olması ve çoklu iç ilişki probleminin ortak çözümü için önerilmiş olan Ridge GM tahmin edicisinde literatürde daha önce önerilmiş olan yanlılık parametrelerinin performansları simülasyon çalışması ve gerçek veri örneği üzerinde incelenmiştir.

Anahtar Kelimeler

Lineer Regresyon Modeli, Çoklu İç İlişki, Aykırı Değer, Ridge Regresyon, Yanlılık Parametresi

Destekleyen Kurum

Eskişehir Osmangazi Üniversitesi

Proje Numarası

2020-19A102

Teşekkür

Bu çalışma, Eskişehir Osmangazi Üniversitesi Bilimsel Araştırma Projeleri (ESOGÜBAP) Komisyonu tarafından 2020-19A102 nolu proje olarak desteklenmiştir.

Comparison of the Performances of Ridge GM Estimators for Different Biased Parameters

Öz

In the multiple linear regression model, commonly encountered problems are multicollinearity and outlier problems. There are many studies about robust biased estimators in the literature to solve these problems simultaneously. The most commonly used of these estimators are robust Ridge estimators. Many studies are still carried out on the Ridge estimator, which depends on the biasing parameter. The performances of the previously proposed biased parameters were compared in the classical Ridge estimator. In this study, we have compared the performances of the biasing parameters for the robust Ridge GM estimators based on the simulation and real data studies.

Anahtar Kelimeler

Linear Regression Model, Multicollinearity, Outlier, Ridge Regression, Biasing Parameter

Proje Numarası

2020-19A102

Kaynakça

• Huber, P. J. (1964). Robust estimation of a location parameter. The Annals of Mathematical Statistics Theory and Methods, 53 (1), 73-101.
• Mallows, C. L. (1975). On some topics in Robustness. Unpublished Memorandum, Bell Telephone Laboratories, Murray Hill, NJ.
• Handschin, E., Schweppe, F. C., Kohlas, J., Fiechter, A. (1975). Bad data analysis for power system state estimation. IEEE Transactions on Power Apparatus and Systems, 4 (2), 105-123.
• Hoerl, A. E., Kennard, R. W. (1970). Ridge regression: biased estimation for nonorthogonal problems. Technometrics,12, 55–67.
• Theobald, C.M. (1974). Generalization of mean square error applied to ridge regression. Journal of the Royal Statistical Society, ser B (36), 103-106.
• Hoerl, A.E., Kennard, R.W., Baldwin, K.F. (1975). Ridge regression: some simulation. Communications in Statistics, 4, 105-123.
• Lawless, J. F., Wang, P. A. (1976). Simulation study of ridge and other regression estimators. Communications in Statistics, Theory and Methods, 5, 307-323.
• Hocking, R. R., Speed, F. M., Lynn, M. J. (1976). A class of biased estimators in linear regression. Technometrics, 18, 425-438.
• Kibria, B.M.G. (2003). Performance of some new ridge regression estimators. Communications in Statistics—Theory and Methods, 32, 419–435.
• Khalaf, G., Shukur, G. (2005). Choosing ridge parameters for regression problems. Communications in Statistics—Theory and Methods, A34, 1177–1182.
• Alkhamisi, M., Khalaf, G., Shukur, G. (2006). Some modifications for choosing ridgeparameters. Communications in Statistics—Theory and Methods,35, 2005–2020.
• Alkhamisi, M. A., Shukur, G. A. (2007). Monte Carlo Study of Recent Ridge Parameters. Communications in Statistics-Simulation and Computation, 36 (3), 535-547.
• Muniz, G., Kibria, B. M. G. (2009). On Some Ridge Regression Estimators: An Empirical Comparisons. Communications in Statistics-Simulation and Computation, 38 (3), 621-630.
• Al-Hassan, Y. M. (2010). Performance of a new ridge regression estimator. Journal of the Association of Arab Universities for Basic and Applied Sciences, 9 (1), 23-26.
• Muniz, G., Kibria, B. M. G., Mansoon, K., Shukur, G. (2012). On developing ridge regression parameters: a graphical investigation. Sort Stat Oper. Res. Trans, 36 (2), 115-138.
• Dorugade, A. V. (2014). New ridge parameters for ridge regression. Journal of the Association of Arab Universities for Basic and Applied Sciences, 15, 94-99.
• Karaibrahimoğlu, A., Asar, Y., Genç, A. (2014). Some new modifications of Kibria’s and Dorugade’s methods: An application to Turkish GDP data. Journal of the Association of Arab Universities for Basic and Applied Sciences, 20, 89-99.
• Asar, Y., Genç, A. (2017). A note on some new modifications of ridge estimators. Kuwait J. Sci.,44 (3), 75-82.
• Silvapulle, M. J. (1991). Robust ridge regression based on an m estimator. Australian Journal of Statistics, 33 (3), 319-333.JJ
• Arslan, O., Billor, N. (1996). Robust ridge estimation based on the gm estimators. Journal of Mathematical and Computational Science 9(1), 1-9.
• Altın Yavuz, A. (2019). A New Modification of Ridge Parameter for Regression Problems: A Monte Carlo Simulation Study, Turkiye Klinikleri Journal of Biostatistics, 11 (3), 173-188.
• Işılar, M. (2020). Çoklu Lineer Regresyon Modelinde Liu tipi GM Tahmin Edicisi, Yayımlanmamış Yüksek Lisans Tezi, Eskişehir Osmangazi Üniversitesi, Eskişehir.
• Simpson, D. G., Rubbert, D., Carrol, R. J. (1992). On one-step Gm estimates and stability of inferences in linear regression. Journal of the American Statistical Association, 87, 439-450.
• Farrar, D. E., Glauber, R. R. (1967). Multicollinearity in regression analysis: The problem revisited. The Review of Economics and Statistics, 49 (1), 92-107.
• Silvey, S. D. (1969). Multicollinearity and imprecise estimation. Journal of the Royal Statistical Society: Series B ( Methodological), 31 (3), 539-552.
• McDonald, G. C., Galarneau, D. I. (1975). A Monte Carlo evaluation of ridge-type estimators. Journal of the American Statistical Association, 70 (350), 407-416.
• Newhouse, J. P., Oman, S. D. (1971). An evaluation of ridge estimators, Rand Corporation (p-716-PR) Santa Monica, 1-16.
• R Core Team (2014). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for statistical computing.
• Brownlee, K. A. (1965). Statistical Theory and Methodology in Science and Engineering 2nd ed, John & Sons, New York.