Constrained linear regression models for symbolic interval-valued variables

Bertrand, P., Goupil, F., Descriptive statistic for symbolic data. In: Bock, H.-H., Diday, E. (Eds.), Analysis of Symbolic Data. Springer, Heidelberg, pp. 106–124 Bock, 2002, Clustering algorithms and Kohonen maps for symbolic data, Journal of the Japanese Society of Computational Statistics, 15, 1 Billard, 2000, Regression analysis for interval-valued data, 369 Billard, 2003, From the statistics of data to the statistics of knowledge: Symbolic data analysis, Journal of American Statistical Association, 98, 470, 10.1198/016214503000242 Billard, L., Chouakria-Douzal, A., Diday, E., 2007. Symbolic Principal Components for Interval-Valued Observations. Technical Report. University of Georgia Bock, 2000, Analysis of symbolic data Cazes, 1997, Extension de l’analyse en composantes principales des donnes de type intervalle, Revue de Statistique Aplique, XLV, 5 Chavent, 1998, A monothetic clustering method, Pattern Recognition Letters, 19, 989, 10.1016/S0167-8655(98)00087-7 Chavent, 2002, Dynamical clustering algorithm of interval data: Optimization of an adequacy criterion based on hausdorff distance, 53 De Carvalho, 1995, Histograms in symbolic data analysis, Annals of Operations Research, 55, 229, 10.1007/BF02030864 De Carvalho, 2007, Fuzzy c-means clustering methods for symbolic interval data, Pattern Recognition Letters, 28, 423, 10.1016/j.patrec.2006.08.014 De Carvalho, 2006, Adaptive Hausdorff distances and dynamic clustering of symbolic data, Pattern Recognition Letters, 27, 167, 10.1016/j.patrec.2005.08.014 Draper, 1981 Dorfman, 2001, Imposing inequality restrictions: Efficiency gains from economic theory, Economics Letters, 71, 205, 10.1016/S0165-1765(01)00362-7 Gowda, 1991, Symbolic clustering using a new dissimilarity measure, Pattern Recognition, 24, 567, 10.1016/0031-3203(91)90022-W Gowda, 1992, Symbolic clustering using a new similarity measure, IEEE Transactions on Systems, Man and Cybernetics, 22, 368, 10.1109/21.148412 Groenen, 2006, I-Scal: Multidimensional scaling of interval dissimilarities, Computational Statistics and Data Analysis, 51, 360, 10.1016/j.csda.2006.04.003 Guru, 2004, Multivalued type proximity measure and concept of mutual similarity value useful for clustering symbolic patterns, Pattern Recognition Letters, 25, 1203, 10.1016/j.patrec.2004.03.016 Guru, 2005, Multivalued type dissimilarity measure and concept of mutual dissimilarity value for clustering symbolic patterns, Pattern Recognition, 38, 151, 10.1016/j.patcog.2003.06.006 Ichino, 1994, Generalized Minkowski metrics for mixed feature type data analysis, IEEE Transactions on Systems, Man and Cybernetics, 24, 698, 10.1109/21.286391 Ichino, 1996, A fuzzy symbolic pattern classifier, 92 Judge, 1966, Inequality restrictions in regression analysis, Journal of the American Statistical Association, 61, 166, 10.1080/01621459.1966.10502016 Lawson, 1974 Lauro, 2000, Principal component analysis of interval data: A symbolic data analysis approach, Computational Statistics, 15, 73, 10.1007/s001800050038 Lauro, 2000, Factorial discriminant analysis on symbolic objects, 212 Liew, 1976, Inequality constrained least-squares estimation, Journal of the American Statistical Association, 71, 746, 10.1080/01621459.1976.10481560 Lima Neto, 2008, Centre and range method to fitting a linear regression model on symbolic interval data, Computational Statistics and Data Analysis, 52, 1500, 10.1016/j.csda.2007.04.014 Lovell, 1970, Multiple regression with inequality constraints: Pretesting bias, hypothesis testing and efficiency, Journal of the American Statistical Association, 65, 913, 10.1080/01621459.1970.10481134 Maia, 2008, Forecasting models for interval-valued time series, Neurocomputing, 71, 3344, 10.1016/j.neucom.2008.02.022 Montgomery, 1982 Palumbo, 2000, Non-symmetrical factorial discriminant analysis for symbolic objects, Applied Stochastic Models in Business and Industry, 15, 419, 10.1002/(SICI)1526-4025(199910/12)15:4<419::AID-ASMB405>3.0.CO;2-P Périnel, 2000, Symbolic discriminant rules, 244 Rasson, 2000, Symbolic kernel discriminant analysis, 240 Scheffé, 1959 Souza, 2004, Clustering of interval data based on city-block distances, Pattern Recognition Letters, 25, 353, 10.1016/j.patrec.2003.10.016