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ROBUST CONFIDENCE INTERVALS IN LINEAR REGRESSION

Year 2010, Volume: 1 Issue: 1, 49 - 56, 29.07.2011

Meral Çetin , Tuba Kavruk

Abstract

Although it is many studies with respect to robust regression methods, there is a few studies with robust confidence interval and tests in the literature. Many of these studies are respect to confidence interval of location parameter. In this study, the aim is compute to confidence intervals for regression parameter and compare to classical confidence interval based on least squares estimator with simulation study, using robust version of parameter and variance, in case of non-normality and outlier.

Keywords

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References

  • Adrover, J., Sal bian-Barrera, M. and Zamar, R. (2004). Globally Robust Inference for the Location and Simple Linear Regression Models. Journal of Statistical Planning and Inference 119, 353- 375.
  • Candan, M. (1995). Doğrusal Regresyon Çözümlemesinde Sağlam Kestiriciler, Bilim Uzmanlığı Tezi, Hacettepe Üniversitesi Fen Bilimleri Enstitüsü. Ankara, 93s.
  • Du Mond, C. ve Lenth, R.V. (1987). A Robust Confidence Interval for Location. Technometrics 29,211-219.
  • Field, C.A. (1997). Robust regression and small sample confidence intervals. Journal of Statistical Planning and Inference 57,39-48.
  • Field, C. ve Welsh, A.H. (1998). Robust Confidence Intervals for Regression Parameters. Australian &New Zealand Journal of Statistic 40, 53-65.
  • Field, C.A. ve Zhou, J. (2003). Confidence Intervals Based On Robust Regression. Journal of Statisti- cal Planning and Inference 115, 425-439.
  • Gross, A.M. (1977). Confidence Intervals for Bisquare Regression Estimates. Jour. Amer. Statics. Assoc. 72, 341-354.
  • Huber, P.J. (1981). Robust Statistics, John Wiley and Sons, New York, 308p.
  • Rouseeuw, P.J. ve Leroy, A.M. (1987). Robust Regression and Outlier Detection. John Wiley and Sons, New York,329p.
  • Ryan, T.P. (1997). Modern Regression Methods. John Wiley and Sons, New York, 515p.
  • Tiku, M.L., Tan, W.Y. ve Balakrishnan, N. (1986). Robust Inference. Marcel Dekker, New York and Basel, 295p.

Year 2010, Volume: 1 Issue: 1, 49 - 56, 29.07.2011

Meral Çetin , Tuba Kavruk

Abstract

References

  • Adrover, J., Sal bian-Barrera, M. and Zamar, R. (2004). Globally Robust Inference for the Location and Simple Linear Regression Models. Journal of Statistical Planning and Inference 119, 353- 375.
  • Candan, M. (1995). Doğrusal Regresyon Çözümlemesinde Sağlam Kestiriciler, Bilim Uzmanlığı Tezi, Hacettepe Üniversitesi Fen Bilimleri Enstitüsü. Ankara, 93s.
  • Du Mond, C. ve Lenth, R.V. (1987). A Robust Confidence Interval for Location. Technometrics 29,211-219.
  • Field, C.A. (1997). Robust regression and small sample confidence intervals. Journal of Statistical Planning and Inference 57,39-48.
  • Field, C. ve Welsh, A.H. (1998). Robust Confidence Intervals for Regression Parameters. Australian &New Zealand Journal of Statistic 40, 53-65.
  • Field, C.A. ve Zhou, J. (2003). Confidence Intervals Based On Robust Regression. Journal of Statisti- cal Planning and Inference 115, 425-439.
  • Gross, A.M. (1977). Confidence Intervals for Bisquare Regression Estimates. Jour. Amer. Statics. Assoc. 72, 341-354.
  • Huber, P.J. (1981). Robust Statistics, John Wiley and Sons, New York, 308p.
  • Rouseeuw, P.J. ve Leroy, A.M. (1987). Robust Regression and Outlier Detection. John Wiley and Sons, New York,329p.
  • Ryan, T.P. (1997). Modern Regression Methods. John Wiley and Sons, New York, 515p.
  • Tiku, M.L., Tan, W.Y. ve Balakrishnan, N. (1986). Robust Inference. Marcel Dekker, New York and Basel, 295p.

Teorik Bilimler

Year 2010, Volume: 1 Issue: 1, 49 - 56, 29.07.2011

Meral Çetin , Tuba Kavruk

Abstract

Sağlam regresyon yöntemlerine ilişkin çok sayıda çalışma olmasına rağmen, regresyon parametrelerinin sağlam güven aralığına ve testlerine ilişkin çalışmalar az sayıdadır. Bu çalışmaların çoğu da konum parametresinin güven aralığı üzerinedir. Bu çalışmada, doğrusal regresyon analizinde normallikten sapmalar ve aykırı değer varlığında, parametre tahminlerinin ve varyanslarının sağlam(robust) versiyonları kullanılarak β-parametrelerinin sağlam güven aralıkları hesaplanmış ve bu aralıklar En Küçük Kareler (EKK) yöntemine dayalı klasik güven aralıkları ile bir benzetim çalışması ile karşılaştırılmıştır

Keywords

Güven aralıkları Sağlam regresyon Sağlam kestiriciler M-kestiriciler

References

  • Adrover, J., Sal bian-Barrera, M. and Zamar, R. (2004). Globally Robust Inference for the Location and Simple Linear Regression Models. Journal of Statistical Planning and Inference 119, 353- 375.
  • Candan, M. (1995). Doğrusal Regresyon Çözümlemesinde Sağlam Kestiriciler, Bilim Uzmanlığı Tezi, Hacettepe Üniversitesi Fen Bilimleri Enstitüsü. Ankara, 93s.
  • Du Mond, C. ve Lenth, R.V. (1987). A Robust Confidence Interval for Location. Technometrics 29,211-219.
  • Field, C.A. (1997). Robust regression and small sample confidence intervals. Journal of Statistical Planning and Inference 57,39-48.
  • Field, C. ve Welsh, A.H. (1998). Robust Confidence Intervals for Regression Parameters. Australian &New Zealand Journal of Statistic 40, 53-65.
  • Field, C.A. ve Zhou, J. (2003). Confidence Intervals Based On Robust Regression. Journal of Statisti- cal Planning and Inference 115, 425-439.
  • Gross, A.M. (1977). Confidence Intervals for Bisquare Regression Estimates. Jour. Amer. Statics. Assoc. 72, 341-354.
  • Huber, P.J. (1981). Robust Statistics, John Wiley and Sons, New York, 308p.
  • Rouseeuw, P.J. ve Leroy, A.M. (1987). Robust Regression and Outlier Detection. John Wiley and Sons, New York,329p.
  • Ryan, T.P. (1997). Modern Regression Methods. John Wiley and Sons, New York, 515p.
  • Tiku, M.L., Tan, W.Y. ve Balakrishnan, N. (1986). Robust Inference. Marcel Dekker, New York and Basel, 295p.
There are 11 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Meral Çetin

Tuba Kavruk This is me

Publication Date July 29, 2011
Published in Issue Year 2010 Volume: 1 Issue: 1

Cite

APA Çetin, M., & Kavruk, T. (2011). ROBUST CONFIDENCE INTERVALS IN LINEAR REGRESSION. Anadolu University Journal of Science and Technology B - Theoretical Sciences, 1(1), 49-56.
AMA Çetin M, Kavruk T. ROBUST CONFIDENCE INTERVALS IN LINEAR REGRESSION. AUBTD-B. July 2011;1(1):49-56.
Chicago Çetin, Meral, and Tuba Kavruk. “ROBUST CONFIDENCE INTERVALS IN LINEAR REGRESSION”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 1, no. 1 (July 2011): 49-56.
EndNote Çetin M, Kavruk T (July 1, 2011) ROBUST CONFIDENCE INTERVALS IN LINEAR REGRESSION. Anadolu University Journal of Science and Technology B - Theoretical Sciences 1 1 49–56.
IEEE M. Çetin and T. Kavruk, “ROBUST CONFIDENCE INTERVALS IN LINEAR REGRESSION”, AUBTD-B, vol. 1, no. 1, pp. 49–56, 2011.
ISNAD Çetin, Meral - Kavruk, Tuba. “ROBUST CONFIDENCE INTERVALS IN LINEAR REGRESSION”. Anadolu University Journal of Science and Technology B - Theoretical Sciences 1/1 (July 2011), 49-56.
JAMA Çetin M, Kavruk T. ROBUST CONFIDENCE INTERVALS IN LINEAR REGRESSION. AUBTD-B. 2011;1:49–56.
MLA Çetin, Meral and Tuba Kavruk. “ROBUST CONFIDENCE INTERVALS IN LINEAR REGRESSION”. Anadolu University Journal of Science and Technology B - Theoretical Sciences, vol. 1, no. 1, 2011, pp. 49-56.
Vancouver Çetin M, Kavruk T. ROBUST CONFIDENCE INTERVALS IN LINEAR REGRESSION. AUBTD-B. 2011;1(1):49-56.
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