Fuzzy data treated as functional data: A one-way ANOVA test approach

Computational Statistics and Data Analysis

Volumn 56, Issue 4, 2012, Pages 943-955

  González Rodríguez, Gil ^a   Colubi, Ana ^b   Gil, María Ángeles ^b  

^a EUROPEAN CENTRE FOR SOFT COMPUTING   (Spain)

^b UNIVERSITY OF OVIEDO   (Spain)

Author keywords

ANOVA statistic; Bootstrap; Convex cone; Functional data; Fuzzy data; Hilbert space; k samples test; Local alternatives

Indexed keywords

BOOTSTRAP; CONVEX CONE; FUNCTIONAL DATAS; FUZZY DATA; HILBERT; K-SAMPLES TEST; LOCAL ALTERNATIVES;

CONES; HILBERT SPACES; REAL VARIABLES;

ANALYSIS OF VARIANCE (ANOVA);

EID: 84856734042     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2010.06.013     Document Type: Article

References (38)

1. I.E. Allen, and C.A. Seaman Likert scales and data analyses Qual. Prog 40 2007 64 65
2. S. Ammar, and R. Wright Applying fuzzy-set theory to performance evaluation Socio-Econ. Plan. Sci. 34 2000 285 302
3. J. Cao, and J.O. Ramsay Generalized profiling estimation for global and adaptive penalized spline smoothing Comput. Statist. Data Anal. 53 2009 2550 2562
4. C. Castaing, and M. Valadier Convex Analysis and Measurable Multifunctions Lec. Notes in Math. vol. 580 1977 Springer-Verlag Berlin
5. J.R. Chimka, and H. Wolfe History of ordinal variables before 1980 Scientific Research and Essays 4 2009 853 860
6. A. Colubi Statistical inference about the means of fuzzy random variables: applications to the analysis of fuzzy- and real-valued data Fuzzy Sets and Systems 160 2009 344 356
7. A. Colubi, J.S. Domnguez-Menchero, M. Lpez-Daz, and D.A. Ralescu On the formalization of fuzzy random variables Inform. Sci. 133 2001 3 6 (Pubitemid 32380828)
8. DE [ 0, 1 ] -representation of random upper semicontinuous functions Proc. Amer. Math. Soc. 130 2002 3237 3242
9. A. Colubi, and G. Gonzlez-Rodrguez Triangular fuzzification of random variables and power of distribution tests: empirical discussion Comput. Statist. Data Anal. 51 2007 4742 4750 (Pubitemid 46560924)
10. A. Cuevas, M. Febrero, and R. Fraiman An anova test for functional data Comput. Statist. Data Anal. 47 2004 111 122
11. A. Cuevas, M. Febrero, and R. Fraiman On the use of the bootstrap for estimating functions with functional data Comput. Statist. Data Anal. 51 2006 1063 1074 (Pubitemid 44635882)
12. E. Fernndez, M. Fernndez, S. Anadn, G. Gonzlez-Rodrguez, and A. Colubi Flood analysis: on the automation of the geomorphological-historical method Combining Soft Computing and Statistical Methods in Data Analysis. Advances in Intelligent and Soft Computing Series vol. 77 2010 Springer-Verlag Berlin, Heidelberg 239 246
13. F. Ferraty, and P. Vieu Nonparametric Functional Data Analysis: Theory and Practice 2006 Springer-Verlag New York
14. F. Ferraty, and P. Vieu Additive prediction and boosting for functional data Comput. Statist. Data Anal. 53 2009 1400 1413
15. M.A. Gil, M. Montenegro, G. Gonzlez-Rodrguez, A. Colubi, and M.R. Casals Bootstrap approach to the multi-sample test of means with imprecise data Comput. Statist. Data Anal. 51 2006 148 162 (Pubitemid 44634803)
16. E. Gin, and J. Zinn Bootstrapping general empirical measures Ann. Probab. 18 1990 851 869
17. W. Gonzlez-Manteiga, and P. Vieu Guest editors of the special issue on statistics for functional data Comput. Statist. Data Anal. 51 2007 4788 5008
18. G. Gonzlez-Rodrguez, A. Colubi, and M.A. Gil A fuzzy representation of random variables: an operational tool in exploratory analysis and hypothesis testing Comput. Statist. Data Anal. 51 2006 163 176 (Pubitemid 44634796)
19. G. Gonzlez-Rodrguez, M. Montenegro, A. Colubi, and M.A. Gil Bootstrap techniques and fuzzy random variables: synergy in hypothesis testing with fuzzy data Fuzzy Sets and Systems 157 2006 2608 2613 (Pubitemid 44301500)
20. R. Krner An asymptotic α-test for the expectation of random fuzzy variables J. Statist. Plann. Inference 83 2000 331 346
21. R. Krner, and W. Nther On the variance of random fuzzy variables C. Bertoluzza, M.A. Gil, D.A. Ralescu, Statistical Modeling, Analysis and Management of Fuzzy Data 2002 Physica-Verlag Heidelberg 22 39
22. R.G. Laha, and V.K. Rohatgi Probability Theory 1979 Wiley New York
23. R. Likert A technique for the measurement of attitudes Arch. Psychol. 140 1932 1 55
24. M.A. Lubiano, M.A. Gil, M. Lpez-Daz, and M.T. Lpez-Garca The λ Combining right arrow above -mean squared dispersion associated with a fuzzy random variable Fuzzy Sets and Systems 111 2000 307 317
25. M. Montenegro, M.R. Casals, M.A. Lubiano, and M.A. Gil Two-sample hypothesis tests of means of a fuzzy random variable Inform. Sci 133 2001 89 100 (Pubitemid 32380833)
26. M. Montenegro, A. Colubi, M.R. Casals, and M.A. Gil Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable Metrika 59 2004 31 49 (Pubitemid 40549717)
27. H.-G. Mller Functional modelling and classification of longitudinal data Scandinavian J. Statist. 32 2005 223 240
28. H.-G. Mller, and W. Yang Dynamic relations for sparsely sampled Gaussian processes (invited paper with discussions) Test 19 2010 1 65
29. H.T. Nguyen A note on the extension principle for fuzzy sets J. Math. Anal. Appl. 64 1978 369 380
30. M.L. Puri, and D.A. Ralescu Differentials of fuzzy functions J. Math. Anal. Appl. 91 1983 552 558
31. M.L. Puri, and D.A. Ralescu The concept of normality for fuzzy random variables Ann. Probab. 11 1985 1373 1379
32. M.L. Puri, and D.A. Ralescu Fuzzy random variables J. Math. Anal. Appl. 114 1986 409 422
33. J.O. Ramsay, and B.W. Silverman Functional Data Analysis 1997 Springer-Verlag New York
34. J.O. Ramsay, and B.W. Silverman Applied Functional Data Analysis 2002 Springer-Verlag New York
35. S.S. Stevens On the theory of scales of measurement Science 103 2884 1946 677 680
36. W. Trutschnig, G. Gonzlez-Rodrguez, A. Colubi, and M.A. Gil A new family of metrics for compact, convex (fuzzy) sets based on a generalized concept of mid and spread Inform. Sci. 179 2009 3964 3972
37. F. Yao, H.-G. Mller, and J.-L. Wang Functional linear regression analysis for longitudinal data Ann. Statist. 33 2005 2873 2903 (Pubitemid 43384879)
38. L.A. Zadeh The concept of a linguistic variable and its application to approximate reasoning, Part 1 Inform. Sci. 8 1975 199 249 Part 2. Inform. Sci. 8, 301353; Part 3. Inform. Sci. 9, 4380