A study on fuzzy robust regression and its application to insurance

tank, fatih; ERBAY DALKILIÇ, Türkan; ŞANLI KULA, KAMİLE

A study on fuzzy robust regression and its application to insurance

Kamile ŞANLI KULA, (Ahi Evran Üniversitesi, Matematik Bölümü, Kırşehir, Türkiye)

Fatih TANK, (Ankara Üniversitesi, İstatistik Bölümü, Ankara, Türkiye)

Türkan ERBAY DALKILIÇ (Karadeniz Teknik Üniversitesi, Fen Edebiyat Fakültesi, İstatistik ve Bilgisayar Bilimleri Bölümü, Trabzon, Türkiye)

Mathematical and Computational Applications

2 0

Yıl: 2012 Cilt: 17 Sayı: 3 Sayfa Aralığı: 223 - 234 Metin Dili: İngilizce İndeks Tarihi: 29-07-2022

A study on fuzzy robust regression and its application to insurance

Öz:

In this study, a fuzzy robust regression method is proposed to constructa model that describes the relation between dependent and independent variables ininsurance. Fuzzy robust regression suggested as an alternative to not only ordinary leastsquares but also classical robust regression. Fuzzy robust regression is finallyinvestigated and discussed by an example with real data arose from a well-knowninsurance company in Turkey.

Anahtar Kelime:

Konular: Matematik

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

1. W.D. Berry, S. Feldman, Multiple Regression in Practice, Sage University Papers Series, Quantitative Applications in the Social Sciences, No. 07-050, 1985.
2. P.T. Chang, and E.S. Lee, A generalized fuzzy weighted least-squares regression, Fuzzy Sets and Systems 82: 289-298, 1996.
3. Y.H.O. Chang, Hybrid fuzzy least-squares regression analysis and its reliability measures. Fuzzy Sets and Systems 119: 225-246, 2001.
4. T.E. Dalkilic, F. Tank, and K.S. Kula, Neural networks approach for determining total claim amounts in insurance, Insurance: Mathematics and Economics 45: 236-241, 2009.
5. R.N. Dave, and R. Krishnapuram, Robust clustering methods: A unified view, IEEE Transactions on Fuzzy Systems 5: 270-293, 1997.
6. P. Diamond, Fuzzy least squares, Information Science 46: 141-157, 1988.
7. J. Fox, An R and S-PLUS Companion to Applied Regression, Sage Publications, 2002.
8. D. N. Gujarati, Essentials of Econometrics, St. Louis, MO: McGraw-Hill, Inc., 1992.
9. F.R., Hampel, E.M., Ronchetti, Rousseeuw, P.J. and Stahel, W.A, Robust statistics, John Willey & Sons, New-York, 1986.
10. P.J. Huber, Robust Estimation of a Location Parameter, Annals of Mathematical Statistics 35: 73-101, 1964.
11. P.J. Huber, Robust Statistics, John Willey & Son, New York (1981).
12. W. L. Hung and M. S. Yang, An omission approach for detecting outliers in fuzzy regression models, Fuzzy Sets and Systems 157: 3109-3122 (2006).
13. H. Huynh, A comparison of four approaches to robust regression, Psychological Bulletin 92: 505-512 (1982).
14. R.V. Hogg, Statistical robustness: one view of its use in applications today, The American Statistican 33: 108-115 (1979).
15. K.S., Kula, A. Apaydin, Fuzzy Robust Regression Analaysis Based on the Ranking of Fuzzy Sets, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems (IJUFKS) 16: 663-681 (2008).
16. M.M. Nasrabadi and E. Nasrabadi, A Mathematical-programming approach to fuzzy linear regression analysis, Applied Mathematics and Computation 163: 977-989 (2004).
17. E. Nasrabadi, S. M. Hashemi and M. Ghatee, An LP approach to outliers detection in fuzzy regression analysis, Int. J. Uncertainty, Fuzziness and Knowledge-Based Systems (IJUFKS) 15: 441-456 (2007).
18. D.T. Redden and W.H. Woddall, Futher examination of fuzzy linear regression, Fuzzy Sets and Systems 79: 203-211 (1996).
19. P. Rousseeuw, B. Daniels, A.Leroy, Applying robust regression to insurance, Insurance: Mathematics and Economics 3: 67-72 (1984).
20. P.J. Rousseuw, and A.M. Leroy, Robust regression and outlier detection, John Wiley & Sons New York (1997).
21. K. Sanli, A. Apaydin, The fuzzy robust regression analysis, the case of fuzzy data set has outlier, G.U.Journal of Science 17: 71-84 (2004).
22. H. Tanaka, S. Uegima and K. Asai, Linear regression analysis with fuzzy model, IEEE Trans. Systems Man Cybernet 12: 903-907 (1982).
23. R. Xu, and C. Li, Multidimensional least-squares fitting with a fuzzy model, Fuzzy Sets and Systems 119: 215-223 (2001).
24. S. Weisberg, Applied Linear Regression (Third Edition), John Willey & Son, Hoboken, New Jersey (2005).
25. M. S. Yang and C. H. Ko, On cluster-wise fuzzy regression analysis, IEEE Transaction on Systems, Man and Cybernetics Part B: Cybernetics 27: 1-13 (1997).
26. M.S. Yang, and T.S. Lin, Fuzzy least-squares linear regression analysis for fuzzy input-output data, Fuzzy Sets and Systems 126: 389-399 (2002).

APA	ŞANLI KULA K, tank f, ERBAY DALKILIÇ T (2012). A study on fuzzy robust regression and its application to insurance. , 223 - 234.
Chicago	ŞANLI KULA KAMİLE,tank fatih,ERBAY DALKILIÇ Türkan A study on fuzzy robust regression and its application to insurance. (2012): 223 - 234.
MLA	ŞANLI KULA KAMİLE,tank fatih,ERBAY DALKILIÇ Türkan A study on fuzzy robust regression and its application to insurance. , 2012, ss.223 - 234.
AMA	ŞANLI KULA K,tank f,ERBAY DALKILIÇ T A study on fuzzy robust regression and its application to insurance. . 2012; 223 - 234.
Vancouver	ŞANLI KULA K,tank f,ERBAY DALKILIÇ T A study on fuzzy robust regression and its application to insurance. . 2012; 223 - 234.
IEEE	ŞANLI KULA K,tank f,ERBAY DALKILIÇ T "A study on fuzzy robust regression and its application to insurance." , ss.223 - 234, 2012.
ISNAD	ŞANLI KULA, KAMİLE vd. "A study on fuzzy robust regression and its application to insurance". (2012), 223-234.

APA	ŞANLI KULA K, tank f, ERBAY DALKILIÇ T (2012). A study on fuzzy robust regression and its application to insurance. Mathematical and Computational Applications, 17(3), 223 - 234.
Chicago	ŞANLI KULA KAMİLE,tank fatih,ERBAY DALKILIÇ Türkan A study on fuzzy robust regression and its application to insurance. Mathematical and Computational Applications 17, no.3 (2012): 223 - 234.
MLA	ŞANLI KULA KAMİLE,tank fatih,ERBAY DALKILIÇ Türkan A study on fuzzy robust regression and its application to insurance. Mathematical and Computational Applications, vol.17, no.3, 2012, ss.223 - 234.
AMA	ŞANLI KULA K,tank f,ERBAY DALKILIÇ T A study on fuzzy robust regression and its application to insurance. Mathematical and Computational Applications. 2012; 17(3): 223 - 234.
Vancouver	ŞANLI KULA K,tank f,ERBAY DALKILIÇ T A study on fuzzy robust regression and its application to insurance. Mathematical and Computational Applications. 2012; 17(3): 223 - 234.
IEEE	ŞANLI KULA K,tank f,ERBAY DALKILIÇ T "A study on fuzzy robust regression and its application to insurance." Mathematical and Computational Applications, 17, ss.223 - 234, 2012.
ISNAD	ŞANLI KULA, KAMİLE vd. "A study on fuzzy robust regression and its application to insurance". Mathematical and Computational Applications 17/3 (2012), 223-234.