A Comparison of Performances of the Estimations of the Bias Parameter in the Quantile Regression Analysis Based on Ridge Estimation

Year 2019, Volume: 1 Issue: 2, 103 - 111, 09.12.2019

Murat Erişoğlu , Nurullah Yaman

Abstract

In this study, the solution of the
multicollinearity problem was investigated in the quantile regression which is
used as an alternative to the least squares regression in case the outliers.
The ridge regression approach was used to solve the multicollinearity problem
in quantile regression. In the quantile regression based on ridge estimation,
the performance of some bias parameter estimates was compared according to the
mean error squares. According to the results of the simulation study, the bias
parameter estimators proposed by Hocking, Speed and Lynn (1976) and Kibria
(2003) showed a more successful performance.

Keywords

Quantile regression, Ridge regression, Multicollinearity, Outliers, Cross validation

Ridge Tahminine Dayalı Kantil Regresyon Analizinde Yanlılık Parametresi Tahminlerinin Performanslarının Karşılaştırılması

Abstract

Bu çalışmada aykırı gözlemlerin
varlığında en küçük kareler regresyonuna alternatif olarak kullanılan kantil
regresyonunda çoklu bağlantı probleminin çözümü ele alınmıştır. Kantil
regresyonunda çoklu bağlantı probleminin çözümünde ridge regresyon yaklaşımı
kullanılmıştır. Ridge tahminine dayalı kantil regresyonunda bazı yanlılık
parametre tahminlerinin performansı hata kareler ortalamasına göre
karşılaştırılmıştır.  Simülasyon
çalışması sonuçlarına göre Hocking, Speed ​​ve Lynn (1976) ile Kibria (2003)
tarafından önerilen yanlılık parametre tahmin edicileri daha başarılı bir
performans göstermişlerdir.

Keywords

Kantil regresyon, Ridge regresyonu, Çoklu bağlantı, Aykırı gözlem, Çapraz doğruluk

References

• [1] R. C. Pfaffenberger, T. E. Dielman, A comparison of regression estimators when both multicollinearity and outliers, içinde: K. D. Lawrence, J. L. Arthur (Ed.) Robust Regression: Analysis and applications, Marcer Dekker Inc. New york and Basel, (1990) 243-270.
• [2] A. E. Hoerl, R. W. Kennard, Ridge regression: Biased estimation for non-orthogonal problems. Technometrics, 12(1) (1970) 55-67. doi: 10.1080/00401706.1970.10488634
• [3] M. S. Suhail, Chand, B. M. G. Kibria, Quantile based estimation of biasing parameters in ridge regression model, Communications in Statistics-Simulation and Computation, (2019) doi: 10.1080/03610918.2018.1530782
• [4] A. A. Yavuz, E. G. Aşık, Kantil Regresyon, Uluslararası Mühendislik Araştırma ve Geliştirme Dergisi, 9(2) (2017) 137-146. doi: 10.29137/umagd.352530
• [5] C. Chen, An introduction to quantile regression and the QUANTREG procedure, In Proceedings of the Thirtieth Annual SAS Users Group International Conference, SAS Institute Inc. Cary, NC. 2005, 213-30.
• [6] R. Koenker, G. Basset, Regression Quantiles, Econometrica 46 (1)(1978) 33-50. doi: 10.2307/1913643.
• [7] R. Koenker, K. F. Hallock, Quantile Regression, Journal of Economic Perspectives 15 (4)(2001) 143-156. doi: 10.1257/jep.15.4.143.
• [8] D. Baur, M. Saisana, N. Schulze, Modelling the effects of meteorological variables on ozone concentration: a quantile regression approach, Atmospheric Environment, 38(28) (2004) 4689-4699. doi: 10.1016/j.atmosenv.2004.05.028
• [9] İ. Altındağ, Quantile regresyon ve bir uygulama, Yüksek Lisans Tezi, Selçuk Üniversitesi Fen Bilimleri Enstitüsü, İstatistik Ana Bilim Dalı, Konya, 2010.
• [10] A. S. Bager, Ridge Parameter in Quantile Regression Models: An Application in Biostatistics, International Journal of Statistics and Applications, 8(2) (2018) 72-78. doi: 10.5923/j.statistics.20180802.06
• [11] H. Zaikarina, A. Djuraidah, A. H. Wigena, Lasso and Ridge Quantile Regression using Cross Validation to Estimate Extreme Rainfall, Global Journal of Pure and Applied Mathematics, 12 (3) (2016) 3305–3314.
• [12] Z. Zeebari, Developing ridge estimation method for median regression, Journal of Applied Statistics, 39(12) (2012) 2627-2638. doi: 10.1080/02664763.2012.724663
• [13] A. E. Hoerl, R. W. Kennard, K. F. Baldwin, Ridge regression: Some simulations. Communications in Statistics, 4(2) (1975) 105-123. doi:10.1080/03610927508827232
• [14] J. F. Lawless, P. Wang, A simulation study of ridge and other regression estimators, Communications in Statistics – Theory and Methods, 5(4)(1976) 307-323. doi: 10.1080/03610927608827353
• [15] R. R. Hocking, F. M. Speed, M. J. Lynn, (1976). A class of biased estimators in linear regression, Technometrics, 18(4) (1976) 55-67. doi:10.1080/00401706.1976.10489474
• [16] B.M. G. Kibria, Performance of some new ridge regression estimators, Communications in Statistics – Simulation and Computation, 32(2) (2003) 419-435. doi: 10.1081/SAC-120017499
• [17] G. Khalaf, G. Shukur, Choosing ridge parameters for regression problems, Communications in Statistics – Theory and Methods, 34(5) (2005) 1177-1182. doi: 10.1081/STA-200056836
• [18] D. G. Gibbons, A Simulation Study of Some Ridge Estimators, Journal of the American Statistical Association, 76 (1981) 131-139. doi: 10.1080/01621459.1981.10477619
• [19] G. C. McDonald, D. I. Galarneau, A Monte Carlo Evaluation of Some Ridge-Type Estimators, Journal of the American Statistical Association, 70 (350) (1975) 407-416. doi: 10.1080/01621459.1975.10479882
• [20] R. H. Myers, Classical and modern regression with applications, Second Edition, Belmont, CA: Duxbury press,1990.