SAĞLAM RİDGE REGRESYON ANALİZİ VE BİR UYGULAMA

Çoklu regresyon analizinde doğrusal bağıntı problemi En Küçük Kareler(EKK) tekniğiyle regresyon parametrelerinin tahmininde güvenilir olmayan sonuçlar verir. Diğer taraftan veri kümesinin aykırı değerler içermesi EKK tahmin edicisinin en iyi, yansız, tutarlı olma özelliğini yitirmesine neden olur. Bu iki problemin aynı veri kümesinde yer alması durumunda sağlam tahmin ediciler üzerinde temellenen yanlı teknikler kullanılması önerilir. Bu çalışmada hem x hem de y yönünde aykırı değer içeren bir veri kümesi için sağlam tahmin edicilerden M, En Küçük Kırpılmış Kareler, En Küçük Medyan Kareler, S ve Genelleştirilmiş M üzerinde temellenen ridge regresyon analizi üzerinde durulmuş ve karşılaştırmalı olarak sonuçları incelenmiştir.

The problem of multicollinearity in multiple linear regression analysis gives unreliable estimates for regression parameters with least squares methods. In addition, outliers in data set cause to lose characteristics of best, unbiased, consistent of least squares estimation. In the presence of multicollinearity and outliers in the data set, it is suggested using biased methods based on robust estimators. In this study, for the data set including outliers both x and y directed, ridge regression analysis based on some robust techniques (M, Least Trimmed Sums of Squares, Least Median of Squares, S and Generalized M ) is applied and the results are considered as comparatively.

Kaynakça

Arslan O. ve N. Billor (1996), “Robust ridge regression estimation based on the GM estimators”, Journal of Math. and Comp. Sci.(Math Ser.), 9:1, 1-9.

Askin, G.R. ve D.C. Montgomery (1980), “Augmented Robust estimators”, Techonometrics, 22, 333-341.

Dinçer, M.Z. (1993), Türkiye Ekonomisi ve Türkiye Ekonomisinde Turizm, Filiz Kitabevi: İstanbul.

Hawkins, D.M. ve D.J. Olive (2002), “In consistency of resampling algorithms for high breakdown regression estimators and a new algorithm”, Journal of the American Statistical Association, 97:136-148.

Hoerl A.E. ve R.W. Kennard (1970), “Ridge regression: Biased estimation for nonorthogonal problems”, Technometrics, 12(1), 55-67.

Hoerl A.E., R.W. Kennard ve K.F. Baldwin (1975), “Ridge Regression: Some simulations”, Commun.Statist. A-Theory Methods, 4, 105-123.

Huber P.J. (1964), “Robust Estimation of a Location Parameter”, Ann. Math. Stat., 35, 73-101.

Huber P.J. (1981), Robust Statistics, Wiley: 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. (1984), “Least Median of Squares Regression”, Journal of the American Statistical Association, 79, 871-880.

Rousseeuw P.J. ve V.J. Yohai (1984), “Robust Regression by Means of S- Estimators”, Robust and Nonlinear Time Series Analysis, eds. J.Franke, W. Hardle, and D. Martin, Springer-Verlag: Heidelberg, Germany, 256-272.

Rousseeuw P.J. ve A.M. Leroy (1987), Robust Regression and Outlier Detection, Wiley: NewYork.

Silvapulle M.J. (1991), “Robust ridge regression based on an M estimator”, Austral.J. Statist., 33(3), 319-333.

Simpson J.R. ve D.C. Montgomery (1998), “A Robust Regression Technique Using Compound Estimation”, Naval Research Logistics, 45, 125-139.

Walker E. (1984), “Influence, Collinearity, and Robust Estimation in Regression”, unpublished Ph.D. dissertation, Department of Statistics, Virginia Polytechnic Institute.

Wisnowski J.W., D.C. Montgomery ve J.R. Simpson (2001), “A Comparative Analysis of Multiple Outlier Detection Procedures in the Linear Regression Model”, Computational Statistics and Data Analysis, 36, 351-382.