Bivariate symbolic regression models for interval-valued variables

Journal of Statistical Computation and Simulation

Volumn 81, Issue 11, 2011, Pages 1727-1744

  Lima Neto, Eufrásio de A ^a   Cordeiro, Gauss M ^b   de Carvalho, Francisco de A T ^c  

^a FEDERAL UNIVERSITY OF PARAÍBA   (Brazil)

^b UNIVERSIDADE FEDERAL RURAL DE PERNAMBUCO   (Brazil)

^c FEDERAL UNIVERSITY OF PERNAMBUCO   (Brazil)

Author keywords

Bivariate symbolic regression method; Deviance; Generalized linear model; Interval valued data; Residual analysis; Symbolic data analysis

Indexed keywords

EID: 84855736117     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/00949655.2010.500470     Document Type: Article

References (33)

1. L. Billard and E. Diday, Symbolic Data Analysis: Conceptual Statistics and Data Mining, John Wiley, New York, 2006.
2. H.-H. Bock and E. Diday, Analysis of Symbolic Data, Exploratory Methods for Extracting Statistical Information from Complex Data, Springer-Verlag, Heidelberg, 2000.
3. E. Diday and M. Fraiture-Noirhomme, Symbolic Data Analysis and the SODAS Software, Wiley-Interscience, Chichester, 2008.
4. P. Bertrand and F. Goupil, Descriptive statistics for symbolic data, in Analysis of Symbolic Data, H.-H Bock and E. Diday, eds., Springer, Heidelberg, 2000, pp. 106-124.
5. L. Billard and E. Diday, From the statistics of data to the statistics of knowledge: Symbolic data analysis, J. Am. Statist. Assoc. 98 (2003), pp. 470-487.
6. F.A.T. De Carvalho, Histograms in symbolic data analysis, Ann. Oper. Res. 55 (1995), pp. 229-322.
7. P. Cazes, A. Chouakria, E. Diday, and S. Schektman, Extension de l'analyse en composantes principales à des données de type intervalle, Rev. Statist. Appl. 24 (1997), pp. 5-24.
8. N.C. Lauro and F. Palumbo, Principal component analysis of interval data: A symbolic data analysis approach, Comput. Stat. 15 (2000), pp. 73-87.
9. F. Palumbo and R. Verde, Non-symmetrical factorial discriminant analysis for symbolic objects, Appl. Stoch. Models Bus. Ind. 15 (2000), pp. 419-427.
10. N.C. Lauro, R. Verde, and F. Palumbo, Factorial discriminant analysis on symbolic objects, in Analysis of Symbolic Data, H.-H Bock and E. Diday, eds., Springer, Heidelberg, 2000, pp. 212-233.
11. A.L.S. Maia, F.A.T De Carvalho, and T.B. Ludermir, Forecasting models for interval-valued time series, Neurocomputing 71 (2008), pp. 3344-3352.
12. P. Groenen, S. Winsberg, O. Rodrigues, and E. Diday, Multidimensional scaling of interval dissimilarities, Comput. Statist. Data Anal. 51 (2006), pp. 360-378.
13. M. Ichino, H. Yaguchi, and E. Diday, A fuzzy symbolic pattern classifier, in Ordinal and Symbolic Data Analysis, E. Diday,Y. Lechevallier and O. Opitz, eds., Springer, Berlin, 1996, pp. 92-102.
14. M. Chavent, A monothetic clustering method, Pattern Recogn. Lett. 19 (1998), pp. 989-996.
15. F.A.T. De Carvalho, R.M.C.R. Souza, M. Chavent, and Y. Lechevallier, Adaptive Hausdorff distances and dynamic clustering of symbolic data, Pattern Recogn. Lett. 27 (2006), pp. 167-179.
16. R.M.C.R. De Souza, and F.A.T. De Carvalho, Clustering of interval data based on city-block distances, Pattern Recogn. Lett. 25 (2004), pp. 353-365.
17. K.C. Gowda and E. Diday, Symbolic clustering using a new dissimilarity measure, Pattern Recogn. 24 (1991), pp. 567-578.
18. D.S. Guru, B.B. Kiranagi, and P. Nagabhushan, Multivalued type proximity measure and concept of mutual similarity value useful for clustering symbolic patterns, Pattern Recogn. Lett. 25 (2004), pp. 1203-1213.
19. F.A.T. De Carvalho, Fuzzy c-means clustering methods for symbolic interval data, Pattern Recogn. Lett. 28 (2007), pp. 423-437.
20. N.R. Draper and H. Smith, Applied Regression Analysis, JohnWiley, NewYork, 1981.
21. D.C. Montgomery and E.A. Peck, Introduction to Linear Regression Analysis, JohnWiley, NewYork, 1982.
22. H. Scheffé, The Analysis of Variance, JohnWiley, NewYork, 1959.
23. P. McCullagh and J. Nelder, Generalized Linear Models, 2nd ed., Chapman & Hall, London, 1989.
24. L. Billard and E. Diday, Regression analysis for interval-valued data, in Data Analysis, Classification and Related Methods: Proceedings of the Seventh Conference of the International Federation of Classification Societies, (IFCS-2000) University of Namur, Belgium, 11-14 July 2000, Springer-Verlag, Heidelberg, 2000, pp. 369-374.
25. E.A. Lima Neto and F.A.T. De Carvalho, Centre and range method to fitting a linear regression model on symbolic interval data, Comput. Stat. Data Anal. 52 (2008), pp. 1500-1515.
26. F. Alfonso, L. Billard, and E. Diday, Symbolic linear regression with taxonomies, in Classification, Clustering and Data Mining Applications, D. Banks, L. House, F.R. McMorris, P. Arabie, andW. Gaul, eds., Springer-Verlag, Berlin, 2004, pp. 429-437.
27. A.L.S. Maia and F.A.T. De Carvalho, Fitting a least absolute deviation regression model on symbolic interval data, in Lecture Notes in Artificial Intelligence: Proceedings of the Ninth Brazilian Symposium on Artificial Intelligence, Springer-Verlag, Berlin, 2008, pp. 207-216.
28. M. Iwasaki and H. Tsubaki, A new bivariate distribution in natural exponential family, Metrika 61 (2005), pp. 323-336.
29. M. Iwasaki and H. Tsubaki, A bivariate generalized linear model with an application to meteorological data analysis, Statist. Methodol. 2 (2005), pp. 175-190.
30. P. D'Urso and T. Gastaldi, A least-square approach to fuzzy linear regression analysis, Comput. Stat. Data Anal. 34 (2000), pp. 427-440.
31. R.D. Cook and S. Weisberg, Residual and Influence in Regression, Springer, Berlin, 1982.
32. A.C. Davison and E.J. Snell, Residuals and diagnostics, Chapman & Hall, London, 1991.
33. R.A. Johnson and D.W. Wichern, Applied Multivariate Statistical Analysis, 6th ed., Prentice Hall, Englewood Cliffs, 2007.