JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Asymptotic Consistency of Least Squares Estimators in Fuzzy Regression Model
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Asymptotic Consistency of Least Squares Estimators in Fuzzy Regression Model
Yoon, Jin-Hee; Kim, Hae-Kyung; Choi, Seung-Hoe;
  PDF(new window)
 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
Fuzzy least squares estimators;asymptotic unbiasedness;asymptotic consistency;
 Language
English
 Cited by
 References
1.
Celmins, A. (1987). Least squares model ¯tting to fuzzy vector data, Fuzzy Sets and Systems, 22, 245-269 crossref(new window)

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 crossref(new window)

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 crossref(new window)

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 crossref(new window)

12.
Korner, R. and Nather, W. (1997). Linear statistical inference for random fuzzy data, Statistics, 29, 221-240 crossref(new window)

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 crossref(new window)

14.
Ming, M., Friedman, M. and Kandel, A. (1997). General fuzzy least squares, Fuzzy Sets and Systems, 88, 107-118 crossref(new window)

15.
Puri, M. L. and Ralescu, D. A. (1986). Fuzzy Random Variables, Journal of Mathematical Analysis and Applications, 114, 409-422 crossref(new window)

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 crossref(new window)

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 crossref(new window)

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 crossref(new window)

21.
Zadeh, L. A. (1965). Fuzzy sets, Information and Control, 8, 338-353 crossref(new window)