A Nonparametric Kernel Approach to Interval-Valued Data Analysis

References

• Ahn, J., Peng, M., Park, C., Jeon, Y. (2012), A Resampling Approach for Interval-Valued Data Regression, Statistical Analysis and Data Mining, 5, 336–348.
   Google Scholar
• Billard, L. (2007), “Dependencies and Variation Components of Symbolic Interval-Valued Data,” in Selected Contributions in Data Analysis and Classification, eds. P. Brito, G. Cucumel, P. Bertrand, and F. de Carvalho, Berlin: Springer-Verlag, pp. 3–13.
   Google Scholar
• Billard, L., and Diday, E. (2000), “Regression Analysis for Interval-Valued Data,” in Data Analysis, Classification, and Related Methods, eds. H. A. L. Kiers, J.-P. Rassoon, P. J. F. Groenen, and M. Schader, Berlin: Springer-Verlag, pp. 369–374.
   Google Scholar
• Billard, L., and Diday, E. (2002), “Symbolic Regression Analysis,” in Classification, Clustering and Data Analysis: Proceedings of the 8th Conference of the International Federation of Classification Societies (IFCS ’02), Poland: Springer, pp. 281–288.
   Google Scholar
• ——— (2007), Symbolic Data Analysis: Conceptual Statistics and Data Mining, Chichester: Wiley.
   Google Scholar
• Blanco-Fernández, A., Colubi, A., García-Bárzana, M. (2012), Confidence Sets in a Linear Regression Model for Interval Data, Journal of Statistical Planning and Inference, 142, 1320–1329.
   Web of Science ®Google Scholar
• ——— (2013), A Set Arithmetic-Based Linear Regression Model for Modelling Interval-Valued Responses Through Real-Valued Variables, Information Sciences, 247, 109–122.
   Web of Science ®Google Scholar
• Blanco-Fernández, A., Corral, N., González-Rodríguez, G. (2011), Estimation of a Flexible Simple Linear Model for Interval Data Based on Set Arithmetic, Computational Statistics and Data Analysis, 55, 2568–2578.
   Web of Science ®Google Scholar
• Cipollini, F., Engle, R.F., Gallo, G.M. (2013), Semiparametric Vector MEM, Journal of Applied Econometrics, 28, 1067–1086.
   Web of Science ®Google Scholar
• Cleveland, W. (1993), Visualizing Data, New Jersey: Hobart Press.
   Google Scholar
• Giordani, P. ( 2011), Lasso-Constrained Regression Analysis for Interval-Valued Data, in Proceedings of the 58th World Statistics Congress of the International Statistical Institute, Dublin, Ireland, pp. 5576–5581.
   Google Scholar
• González-Rodríguez, G., Blanco, A., Corral, N., Colubi, A. (2007), Least Squares Estimation of Linear Regression Models for Convex Compact Random Sets, Advances in Data Analysis and Classification, 1, 67–81.
   Web of Science ®Google Scholar
• Gu, C. (2002), Smoothing Spline ANOVA Models, New York: Springer Verlag.
   Google Scholar
• Jeon, Y. (2012), A Characterization of the Log-Density Smoothing Spline ANOVA Model, Communications in Statistics—Theory and Methods, 41, 2081–2087.
   Web of Science ®Google Scholar
• Kullback, S., Leibler, R. (1951), On Information and Sufficiency, Annals of Mathematical Statistics, 22, 79–86.
   Google Scholar
• Lima Neto, E., Cordeiro, G., de Carvalho, F. (2011), Bivariate Symbolic Regression Models for Interval-Valued Variables, Journal of Statistical Computation and Simulation, 81, 1727–1744.
   Web of Science ®Google Scholar
• Lima Neto, E., de Carvalho, F. (2008). Center and Range Method for Fitting a Linear Regression Model to Symbolic Interval Data, Computational Statistics and Data Analysis, 52, 1500–1515.
   Web of Science ®Google Scholar
• Lima Neto, E.A., Cordeiro, G.M., Carvalho, F. A.T., Anjos, U., and Costa, A. (2009), “Bivariate Generalized Linear Model for Interval-Valued Variables,” in Proceedings 2009 IEEE International Joint Conference on Neural Networks, Vol. 1, Atlanta, USA, pp. 2226–2229.
   Google Scholar
• Silva, A., Lima Neto, E.A., and Anjos, U. (2011), “A Regression Model to Interval-Valued Variables Based on Copula Approach,” in Proceedings of the 58th World Statistics Congress of the International Statistical Institute, Dublin, Ireland, pp. 6481–6486.
   Google Scholar
• Sinova, B., Colubi, A., Gil, M.A., González-Rodríguez, G. (2012), Interval Arithmetic-Based Simple Linear Regression Between Interval Data: Discussion and Sensitivity Analysis on the Choice of the Metric, Information Sciences, 199, 109–124.
   Web of Science ®Google Scholar
• Xu, W. (2010), Symbolic Data Analysis: Interval-Valued Data Regression, Ph.D. dissertation, . University of Georgia.
   Google Scholar