Least squares estimation of a linear regression model with LR fuzzy response

Computational Statistics and Data Analysis

Volumn 51, Issue 1, 2006, Pages 267-286

  Coppi, Renato ^a   D'Urso, Pierpaolo ^b   Giordani, Paolo ^a   Santoro, Adriana ^b  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b UNIVERSITY OF MOLISE   (Italy)

Author keywords

Analysis of uncertainty; Goodness of fit; Least squares approach; LR fuzzy response variable; Multiple linear regression

Indexed keywords

DATA REDUCTION; FUZZY SETS; ITERATIVE METHODS; MATHEMATICAL MODELS; UNCERTAIN SYSTEMS;

ANALYSIS OF UNCERTAINTY; GOODNESS OF FIT; LR FUZZY RESPONSE VARIABLE; MULTIPLE LINEAR REGRESSION;

REGRESSION ANALYSIS;

EID: 33750310787     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2006.04.036     Document Type: Article

References (36)

1. Celminš A. Multidimensional least-squares fitting of fuzzy models. Math. Model. 9 (1987) 669-690
2. Chang Y.H., and Ayyub B.M. Fuzzy regression methods-a comparative assessment. Fuzzy Sets and Systems 119 (2001) 187-203
3. Chang P.T., and Lee E.S. A generalized fuzzy weighted least-squares regression. Fuzzy Sets and Systems 82 (1996) 289-298
4. Coppi R., and D'Urso P. Regression analysis with fuzzy informational paradigm: a least-squares approach using membership function information. Int. J. Pure Appl. Math. 8 3 (2003) 279-306
5. D'Urso P. Linear regression analysis for fuzzy/crisp input and fuzzy/crisp output data. Comput. Statist. Data Anal. 42 1-2 (2003) 47-72
6. D'Urso P., and Gastaldi T. A least-squares approach to fuzzy linear regression analysis. Comput. Statist. Data Anal. 34 (2000) 427-440
7. D'Urso P., and Gastaldi T. An orderwise polynomial regression procedure for fuzzy data. Fuzzy Sets and Systems 130 (2002) 1-19
8. D'Urso P., and Giordani P. Fitting of fuzzy linear regression models with multivariate response. Int. Math. J. 3 6 (2003) 655-664
9. Diamond P. Fuzzy least squares. Inform. Sci. 46 (1988) 141-157
10. Diamond P., and Tanaka H. Fuzzy regression analysis. In: Slowinski R. (Ed). Fuzzy Sets in Decision Analysis, Operations Research and Statistics (1998), Kluwer Academic Publishers, USA, MA 349-387
11. Dubois D., and Prade H. Possibility Theory (1988), Plenum Press, New York
12. Efron B., and Tibshirani R.J. An Introduction to the Bootstrap (1993), Chapman & Hall, New York
13. Flethcher R. Practical Methods of Optimization (1980), Wiley, New York
14. Fomby T., Hill C., and Johnson S.S. Advanced Econometric Methods (1980), Springer, Needham, MA
15. Gelman A., Carlin J., Stern H., and Rubin D. Bayesian Data Analysis (1995), CRC Press, Boca Raton, FL
16. Graybill, F.A., 1961. An Introduction to Linear Statistical Models, vol. 1. Mc-Graw-Hill, New York.
17. Hastie T., Tibshirani R., and Friedman J. The Elements of Statistical Learning-Data Mining, Inference, and Prediction (2001), Springer, New York
18. Kim K.J., Moskovitz H., and Koksalan M. Fuzzy versus statistical linear regression. Eur. J. Oper. Res. 92 (1996) 417-434
19. Körner R., and Näther W. Linear regression with random fuzzy variables: extended classical estimates, best linear estimates, least squares estimates. Inform. Sci. 109 (1998) 95-118
20. Krätschmer V. Least squares estimation in linear regression models with vague concepts. In: Lopez-Diaz M., Gil M.A., Grzegorzewski P., Hryniewicz P., and Lawry J. (Eds). Soft Methodology and Random Information Systems (2004), Springer, Heidelberg 407-414
21. Liew C.K. Inequality constrained least-squares estimation. J. Amer. Statist. Assoc. 71 (1976) 746-751
22. Lopez-Diaz M., and Gil M.A. Constructive definitions of fuzzy random variables. Statist. Probab. Lett. 36 (1997) 135-143
23. Ma M., Friedman M., and Kandel A. General fuzzy least squares. Fuzzy Sets and Systems 88 (1997) 107-118
24. Montenegro M., Casals M.R., Lubiano M.A., and Gil M.A. Two-sample hypothesis tests of means of a fuzzy random variable. Inform. Sci. 133 (2001) 89-100
25. Näther W. On random fuzzy variables of second order and their application to linear statistical inference with fuzzy data. Metrika 51 (2000) 201-221
26. Näther, W., 2007. Regression with fuzzy random data. Comput. Statist. Data Anal., in this issue, doi:10.1016/j.csda.2006.02.021.
27. Neter M., Kutner H., Nachtsheim C.J., and Wasserman W. Applied Linear Statistical Models (1996), Irwin, Chicago
28. Puri M.L., and Ralescu D.A. The concept of normalità for fuzzy random variables. The Ann. Probab. 13 (1985) 1373-1379
29. Puri M.L., and Ralescu D.A. Fuzzy random variables. J. Math. Anal. Appl. 114 (1986) 409-422
30. Tanaka H., Uejima S., and Asai K. Linear regression analysis with fuzzy model. IEEE Trans. Syst. Man Cybernet. 12 (1982) 903-907
31. Tanaka H., and Watada J. Possibilistic linear systems and their application to the linear regression model. Fuzzy Sets and Systems 27 (1988) 275-289
32. Wu H.C. Fuzzy least squares estimators in linear regression analysis for imprecise input and output data. Comput. Statist. Data Anal. 42 (2003) 203-217
33. Wünsche A., and Näther W. Least-squares fuzzy regression with fuzzy random variables. Fuzzy Sets and Systems 130 (2002) 43-50
34. Yang M.S., and Ko C.H. On a class of fuzzy c-numbers clustering procedures for fuzzy data. Fuzzy Sets and Systems 84 (1996) 49-60
35. Zadeh L. Toward a generalized theory of uncertainty (GTU) -an outline. Inform. Sci. 172 (2005) 1-40
36. Zimmermann H.J. Fuzzy Set Theory and its Applications (2001), Kluwer Academic Press, Dordrecht