RİDGE REGRESYONDA M TAHMİN EDİCİLERİNİN KULLANIMI ÜZERİNE BİR UYGULAMA

Year 2011, Volume: 26 Issue: 1, - 2, 25.06.2011

HATİCE Şamkar ÖZLEM Alpu EKREM Altan

Abstract

Bu çalışmada y yönündeki aykırı değerlerin ve çoklu doğrusal bağıntı probleminin varlığında, M tahmin edicilerine dayalı sağlam ridge regresyon analizi ele alınmıştır. Bunun için Türkiye’deki turizm verileri üzerine bir uygulama gerçekleştirilmiş ve M tahmin edicilerine dayalı ridge regresyonun y yönündeki aykırı değerlere karşı sıradan ridge regresyondan daha az duyarlı olduğu gösterilmiştir.

Keywords

M Tahmin Metodu, Ridge Regresyon, Çoklu Bağıntı, Aykırı değer

AN APPLICATION OF RIDGE REGRESSION ON M ESTIMATORS

Abstract

In this study, we examine robust ridge regression analysis based on Huber M type estimators in the presence of multicollinearity and outlier in y direction. To this aim, we apply the analysis on tourism data in Turkey. It has shown that ridge regression based on M estimators is less sensitive than ordinary ridge regression in the presence of outlier in the y direction.

Keywords

M estimation, Ridge Regression, Multicollinearity, Outlier

References

• Arslan, O. ve N. Billor (1996), “Robust ridge regression estimation based on the GM-estimators”, Journal of Math., 9(1), 1-9.
• Askin, G.R. ve D.C. Montgomery (1980), “Augmented Robust estimators”, Techonometrics, 22, 333-341.
• Coşkuntuncel O. (2005), Karma Denemelerde ve Modellerde Robust İstatistiksel Analizler, Çukurova Üniversitesi Fen Bilimleri Enstitüsü, Basılmamış Doktora Tezi, Adana.
• Dempster, A.P., M. Schatzoff ve N.Wermut (1977), “A simulation study of alternatives to ordinary least squares”, Journal of the American Statistical Association, 72, 77-91.
• Firinquatti, L. (1999), “A generalized ridge regression estimator and its finite sample properties”, Commun. Statist. –Theory Meth. 28(5), 1217-1229.
• Hoerl, A.E ve R.W. Kennard (1970a), “Ridge regression: Biased estimation for nonorthogonal problems”, Technometrics, 12, 55-67.
• Hoerl, A.E ve R.W. Kennard (1970b), “Ridge regression: Applications to nonorthogonal problems”, Technometrics, 12, 69-82.
• Hoerl, A.E ve R.W. Kennard (1976), “Ridge regression: Iterative estimation of the biasing parameter”. Commun. Statist.-Theory Meth. A5(1), 77-78.
• Hoerl, A.E ve R.W. Kennard ve K.F. Baldwin (1975), “Ridge regression: Some simulations”, Commun. Statist, 4(2), 105-123.
• Huber, P.J. (1964), “Robust estimation of a location parameter”, Ann. Math. Stat., 35, 73-101.
• Kadiyala, K. (1981), “Bounds for the biasing parameter in ridge regression”, Commun. Statist.-Theory Methods, A10, 2369-2372.
• Kenneth, D.L. ve L.A. Jeffrey (1990), Robust Regression: Analysis and Aplications, Marcel Dekker, Inc.
• Lawless, J.F. ve P. Wang (1976), “A simulation study of ridge and other regression estimators”, Commun. Statist. A5, 307-323.
• Lee, T.Z. ve D.B. Campbell (1985), “Selecting the optimum k in ridge regression”, Commun. Statist.-Theory Meth. 14(7), 1589-1604.
• Maronna R.A., R.D. Martin ve V.J. Yohai (2006), Robust Statistics:Theory and Methods, John Wiley and Sons, New York.
• Montgomery, D.C., E.A. Peck ve G.G. Vining (2001), Introduction to Linear Regression Analysis. John Wiley and Sons, New York.
• Pfaffenberger, R.C. ve T.E. Dielman (1990), A comparison of regression estimators when both multicollinearity and outliers are present. In Robust Regression (ed. Lawrence and Arthur), 243-270.
• Rousseeuw P.J. ve A.M. Leroy (1987), Robust Regression and Outlier Detection, John Wiley and Sons, NewYork.
• Silvapulle, M.J. (1991), “Robust ridge regression based on an M estimator”, Austral. J. Statist, 33, 319-333.
• Tamarkin, M. (1982), “A simulation study of the stochastic ridge k”, Commun. Statist.-Simulation and Computation, 11(2), 159-173.
• Troskie, C.G. ve D.O. Chalton (1996), “A Bayesian estimate for the constants in ridge regression”, South African Statist. J., 30, 119-137.
• Vinod, H.D. ve A. Ullah (1981), Recent Advances in Regression Methods, New York : Dekker.