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REGRESYON ANALİZİNDE KULLANILAN EN KÜÇÜK KARELER VE EN KÜÇÜK MEDYAN KARELER YÖNTEMLERİNİN KARŞILAŞTIRILMASI

Year 2008, Volume: 3 Issue: 2, 219 - 229, 01.12.2008

Abstract

İstatistiksel yöntemler içerisinde yer alan regresyon çözümlemesi en çok
kullanılan yöntemlerden biridir. Olası birçok regresyon yöntemlerinin dışında,
genellikle matematiksel hesaplamalardaki kolaylığından dolayı, En Küçük Kareler
yöntemi (EKK) en uygun tahmin yöntemi olarak kullanılmaktadır. Veri analizi ve
ekonometri uygulamalarında EKK kestiricileri yaygın olarak tercih edilmektedir.
Bununla birlikte EKK kestiricileri sapan değerlere karşı oldukça hassas olduğundan,
veri kümesinin sapan değerler içermesi durumunda veriler hakkında EKK
kestiricileriyle yapılacak yorumlamalar geçersiz ve yanıltıcı olabilmektedir. Bu gibi
durumlarda sapan değerler için önerilen güçlü regresyon yöntemlerini tercih etmek,
sonuçların güvenirliliği açısından daha uygundur. İstatistiksel çözümlemelerde
kullanılan bu güçlü yöntemlerden biri de En Küçük Medyan Kareler yöntemidir
(EKMK). Bu çalışmada, benzetim yoluyla oluşturulan veri kümelerinden yararlanılarak
basit doğrusal regresyon modeli için EKK ve EKMK yöntemlerinden elde edilen model
kestirim değerleri ( 0ˆβ , 1ˆβ , 2 σˆ , R2) karşılaştırılmıştır.

References

  • BARNETT V, LEWIS T, 1994. Outliers in Statistical Data. John Wiley Sons, Canada, pp.7–25.
  • BARRETO H, 2001. An Introduction to Least Median of Squares, www.wabash.edu/econexcel
  • BIRKES D, DODGE Y, 1993. Alternative Methods of Regression. John Wiley Sons, New York, pp.80–140.
  • DAVIES PL, GATHER U, 1993. The Identification of Multiple Outliers. Journal of Statistical Planning and Inference, 122, 65–78.
  • EDELSBRUNNER H, SOUVANIE L, 1990. Computing Least Median of Squares Regression Lines and Guided Topological Sweep. Journal of the American Statistical Association, 85(409), 115–119.
  • ERICKSON J, HAR-PELED S, MOUNT DM, 2006. On the Least Median Square Problem. Discrete Comptutational Geometry. 36, 593–607.
  • FOX J, 1997. Applied Regression Analysis: Linear Models and Related Methods. Sage Publication, USA, pp.123–240.
  • GOODAL C, 1983. Examining Residuals. In: HOAGLIN D & TUKEY J (Eds.) Understanding Robust and Exploratory Data Analysis. John Wiley Sons, Canada, pp.211–242.
  • KLEINBAUM, KUPPER, MULLER, and NIZAM, 1998. Applied Regression Analysis and Other Multivariate Methods. Duxbury, USA.
  • MOHEBBI M, NOURIJELYANI K, ZERAATI H, 2007. A Simulation Study on Robust Alternatives of Least Squares Regression. Journal of Applied Sciences, 7(22), 3469–3476.
  • MONTGOMERY D, HINES W, 1990. Probability and Statistics in Engineering and Management Science, John Wiley Sons, Canada.
  • MOUNT DM, NETANYAHU N, ROMANIK K, SILVERMAN R, WU AY, 2007. A Pratical Approximation Algorithm for The LMS Line Estimator. Computational Statistics and Data Analysis, 51, 2461–2486.
  • NAIR KR, SHRIVASTAVA MP, 1942. On a Simple Method of Curve Fitting. Sankhaya, 6, 121–132.
  • NETER J, KUTNER M, NACHTSHEIM C, and WASSERMAN W, 1996. Applied Lineear Regression Models, Irwin, USA.
  • OLSON CF, 1997. An Approximation Algorithm for Least Median of Squares Regression. Information Processing Letters, 63, 237–241.
  • ORTIZ M, SARABIA L, and HERRERO A, 2006. Robust Regression Techniques: A Useful Alternative for the Detection Data in Chemical Analysis. Talanta, 70, 499–512.
  • ROUSSEEUW JP, 1984. Least Median of Squares Regression. Journal of the American Statistical Association, 79(388), 871–880.
  • ROUSSEEUW P, LEROY A, 1987. Robust Regression and Outlier Detection. John Wiley Sons, Canada, pp. 84–143.
  • RYAN TP, 1997. Modern Regression Methods. John Wiley Sons, New York.
  • WALD A, 1940. The Fitting of Straight Lines if Both Variables are Subject to Error. Annals of Mathematical Statistic, 11, 282–300.
  • WILCOX RR, 1997. Introduction to Robust estimation and Hypothesis Testing. Academic Press. San Diego.
Year 2008, Volume: 3 Issue: 2, 219 - 229, 01.12.2008

Abstract

References

  • BARNETT V, LEWIS T, 1994. Outliers in Statistical Data. John Wiley Sons, Canada, pp.7–25.
  • BARRETO H, 2001. An Introduction to Least Median of Squares, www.wabash.edu/econexcel
  • BIRKES D, DODGE Y, 1993. Alternative Methods of Regression. John Wiley Sons, New York, pp.80–140.
  • DAVIES PL, GATHER U, 1993. The Identification of Multiple Outliers. Journal of Statistical Planning and Inference, 122, 65–78.
  • EDELSBRUNNER H, SOUVANIE L, 1990. Computing Least Median of Squares Regression Lines and Guided Topological Sweep. Journal of the American Statistical Association, 85(409), 115–119.
  • ERICKSON J, HAR-PELED S, MOUNT DM, 2006. On the Least Median Square Problem. Discrete Comptutational Geometry. 36, 593–607.
  • FOX J, 1997. Applied Regression Analysis: Linear Models and Related Methods. Sage Publication, USA, pp.123–240.
  • GOODAL C, 1983. Examining Residuals. In: HOAGLIN D & TUKEY J (Eds.) Understanding Robust and Exploratory Data Analysis. John Wiley Sons, Canada, pp.211–242.
  • KLEINBAUM, KUPPER, MULLER, and NIZAM, 1998. Applied Regression Analysis and Other Multivariate Methods. Duxbury, USA.
  • MOHEBBI M, NOURIJELYANI K, ZERAATI H, 2007. A Simulation Study on Robust Alternatives of Least Squares Regression. Journal of Applied Sciences, 7(22), 3469–3476.
  • MONTGOMERY D, HINES W, 1990. Probability and Statistics in Engineering and Management Science, John Wiley Sons, Canada.
  • MOUNT DM, NETANYAHU N, ROMANIK K, SILVERMAN R, WU AY, 2007. A Pratical Approximation Algorithm for The LMS Line Estimator. Computational Statistics and Data Analysis, 51, 2461–2486.
  • NAIR KR, SHRIVASTAVA MP, 1942. On a Simple Method of Curve Fitting. Sankhaya, 6, 121–132.
  • NETER J, KUTNER M, NACHTSHEIM C, and WASSERMAN W, 1996. Applied Lineear Regression Models, Irwin, USA.
  • OLSON CF, 1997. An Approximation Algorithm for Least Median of Squares Regression. Information Processing Letters, 63, 237–241.
  • ORTIZ M, SARABIA L, and HERRERO A, 2006. Robust Regression Techniques: A Useful Alternative for the Detection Data in Chemical Analysis. Talanta, 70, 499–512.
  • ROUSSEEUW JP, 1984. Least Median of Squares Regression. Journal of the American Statistical Association, 79(388), 871–880.
  • ROUSSEEUW P, LEROY A, 1987. Robust Regression and Outlier Detection. John Wiley Sons, Canada, pp. 84–143.
  • RYAN TP, 1997. Modern Regression Methods. John Wiley Sons, New York.
  • WALD A, 1940. The Fitting of Straight Lines if Both Variables are Subject to Error. Annals of Mathematical Statistic, 11, 282–300.
  • WILCOX RR, 1997. Introduction to Robust estimation and Hypothesis Testing. Academic Press. San Diego.
There are 21 citations in total.

Details

Primary Language Turkish
Journal Section Makaleler
Authors

Özgül Vupa This is me

Özlem Gürünlü Alma This is me

Publication Date December 1, 2008
Published in Issue Year 2008 Volume: 3 Issue: 2

Cite

IEEE Ö. Vupa and Ö. Gürünlü Alma, “REGRESYON ANALİZİNDE KULLANILAN EN KÜÇÜK KARELER VE EN KÜÇÜK MEDYAN KARELER YÖNTEMLERİNİN KARŞILAŞTIRILMASI”, Süleyman Demirel University Faculty of Arts and Science Journal of Science, vol. 3, no. 2, pp. 219–229, 2008, doi: 10.29233/sdufeffd.134658.