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Asymptotic Consistency of Least Squares Estimators in Fuzzy Regression Model

  • Yoon, Jin-Hee (School of Economics, Yonsei University) ;
  • Kim, Hae-Kyung (Department of Mathematics, Yonsei University) ;
  • Choi, Seung-Hoe (School of Liberal Arts and Science, Korea Aerospace University, Korea Aerospace University)
  • Published : 2008.11.30

Abstract

This paper deals with the properties of the fuzzy least squares estimators for fuzzy linear regression model. Especially fuzzy triangular input-output model including error term is proposed. The error term is considered as a fuzzy random variable. The asymptotic unbiasedness and the consistency of the estimators are proved using a suitable metric.

Keywords

References

  1. Celmins, A. (1987). Least squares model ¯tting to fuzzy vector data, Fuzzy Sets and Systems, 22, 245-269 https://doi.org/10.1016/0165-0114(87)90070-4
  2. Chang, P. T. and Lee, E. S. (1994). Fuzzy least absolute deviations regression and the conflicting trends in fuzzy parameters, Computers & Mathematics with Applica-tions, 28, 89-101
  3. Choi, S. S., Hong, D. H. and Kim, D. H. (2000). Fuzzy linear regression model using the least Hausdorff-distance square method, The Korean Communications in Statistics, 7, 643-654
  4. Diamond, P. (1988). Fuzzy least squares, Information Science: An International Journal, 46 , 141-157
  5. Diamond, P. (1989). Fuzzy kriging, Fuzzy Sets and Systems, 33, 315-332 https://doi.org/10.1016/0165-0114(89)90121-8
  6. Diamond, P. and Korner, R. (1997). Extended fuzzy linear models and least squares estimates, Computers & Mathematics with Applications, 33, 15-32
  7. Diamond, P. and Kloeden, P. (1994). Metric Spaces of Fuzzy Sets: Theory and Application, World Scientific Publishing Company, New Jersey
  8. Kao, C. and Chyu, C. L. (1989). A fuzzy linear regression model with better explanatory power, Fuzzy Sets and Systems, 126, 401-409
  9. Kao, C. and Chyu, C. L. (2003). Least-squares estimates in fuzzy regression analysis, European Journal of Operational Research, 148, 426-435 https://doi.org/10.1016/S0377-2217(02)00423-X
  10. Kim, H. K., Yoon, J. H. and Li, Y. (2008). Asymptotic properties of least squares estimation with fuzzy observations, Information Science: An International Journal, 178, 439-451
  11. Korner, R. (1997). On the variance of fuzzy random variables, Fuzzy Sets and Systems, 92, 83-93 https://doi.org/10.1016/S0165-0114(96)00169-8
  12. Korner, R. and Nather, W. (1997). Linear statistical inference for random fuzzy data, Statistics, 29, 221-240 https://doi.org/10.1080/02331889708802586
  13. Korner, R. and Nather, W. (1998). Linear regression with random fuzzy variables: Extended classical estimates, best liner estimates, least squares estimate, Journal of Information Sciences, 109, 95-118 https://doi.org/10.1016/S0020-0255(98)00010-3
  14. Ming, M., Friedman, M. and Kandel, A. (1997). General fuzzy least squares, Fuzzy Sets and Systems, 88, 107-118 https://doi.org/10.1016/S0165-0114(96)00051-6
  15. Puri, M. L. and Ralescu, D. A. (1986). Fuzzy Random Variables, Journal of Mathematical Analysis and Applications, 114, 409-422 https://doi.org/10.1016/0022-247X(86)90093-4
  16. Rohatgi, V. K. (1979). An Introduction to Probability Theory and Mathematical Statistics, John Wiley & Sons, New York
  17. Sakawa, M. and Yano, H. (1992). Multiobjective fuzzy linear regression analysis for fuzzy input-output data, Fuzzy Sets and Systems, 47, 173-181 https://doi.org/10.1016/0165-0114(92)90175-4
  18. Tanaka, H., Uejima, S. and Asai, K. (1982). Linear regression analysis with fuzzy model, IEEE Transactions on Publication Date, 12, 903-907
  19. Yang, M. S. and Lin, T. S. (2002). Fuzzy least-squares linear regression analysis for fuzzy input-output data, Fuzzy Sets and Systems, 126, 389-399 https://doi.org/10.1016/S0165-0114(01)00066-5
  20. Yang, M. and Liu, H. H. (2003). Fuzzy least-squares algorithms for interactive fuzzy linear regression models, Fuzzy Sets and Systems, 135, 305-316 https://doi.org/10.1016/S0165-0114(02)00123-9
  21. Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, 338-353 https://doi.org/10.1016/S0019-9958(65)90241-X