RİDGE REGRESYONDA M TAHMİN EDİCİLERİNİN KULLANIMI ÜZERİNE BİR UYGULAMA

Öz

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.

Anahtar Kelimeler

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

AN APPLICATION OF RIDGE REGRESSION ON M ESTIMATORS

Öz

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.

Anahtar Kelimeler

• M estimation, Ridge Regression, Multicollinearity, Outlier

Kaynakça

1. Arslan, O. ve N. Billor (1996), “Robust ridge regression estimation based on the GM-estimators”, Journal of Math., 9(1), 1-9.
2. Askin, G.R. ve D.C. Montgomery (1980), “Augmented Robust estimators”, Techonometrics, 22, 333-341.
3. Coşkuntuncel O. (2005), Karma Denemelerde ve Modellerde Robust İstatistiksel Analizler, Çukurova Üniversitesi Fen Bilimleri Enstitüsü, Basılmamış Doktora Tezi, Adana.
4. 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.
5. Firinquatti, L. (1999), “A generalized ridge regression estimator and its finite sample properties”, Commun. Statist. –Theory Meth. 28(5), 1217-1229.
6. Hoerl, A.E ve R.W. Kennard (1970a), “Ridge regression: Biased estimation for nonorthogonal problems”, Technometrics, 12, 55-67.
7. Hoerl, A.E ve R.W. Kennard (1970b), “Ridge regression: Applications to nonorthogonal problems”, Technometrics, 12, 69-82.
8. Hoerl, A.E ve R.W. Kennard (1976), “Ridge regression: Iterative estimation of the biasing parameter”. Commun. Statist.-Theory Meth. A5(1), 77-78.

9. Hoerl, A.E ve R.W. Kennard ve K.F. Baldwin (1975), “Ridge regression: Some simulations”, Commun. Statist, 4(2), 105-123.
10. Huber, P.J. (1964), “Robust estimation of a location parameter”, Ann. Math. Stat., 35, 73-101.
11. Kadiyala, K. (1981), “Bounds for the biasing parameter in ridge regression”, Commun. Statist.-Theory Methods, A10, 2369-2372.
12. Kenneth, D.L. ve L.A. Jeffrey (1990), Robust Regression: Analysis and Aplications, Marcel Dekker, Inc.
13. Lawless, J.F. ve P. Wang (1976), “A simulation study of ridge and other regression estimators”, Commun. Statist. A5, 307-323.
14. Lee, T.Z. ve D.B. Campbell (1985), “Selecting the optimum k in ridge regression”, Commun. Statist.-Theory Meth. 14(7), 1589-1604.
15. Maronna R.A., R.D. Martin ve V.J. Yohai (2006), Robust Statistics:Theory and Methods, John Wiley and Sons, New York.
16. Montgomery, D.C., E.A. Peck ve G.G. Vining (2001), Introduction to Linear Regression Analysis. John Wiley and Sons, New York.
17. 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.
18. Rousseeuw P.J. ve A.M. Leroy (1987), Robust Regression and Outlier Detection, John Wiley and Sons, NewYork.
19. Silvapulle, M.J. (1991), “Robust ridge regression based on an M estimator”, Austral. J. Statist, 33, 319-333.
20. Tamarkin, M. (1982), “A simulation study of the stochastic ridge k”, Commun. Statist.-Simulation and Computation, 11(2), 159-173.
21. Troskie, C.G. ve D.O. Chalton (1996), “A Bayesian estimate for the constants in ridge regression”, South African Statist. J., 30, 119-137.
22. Vinod, H.D. ve A. Ullah (1981), Recent Advances in Regression Methods, New York : Dekker.