A generalized Mahalanobis distance for mixed data |
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Authors: | AR de Leon KC Carrière |
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Institution: | a Department of Mathematics & Statistics, University of Calgary, Calgary Alb., Canada T2N 1N4 b Department of Mathematical & Statistical Sciences, 632 Central Academic Building, University of Alberta, Edmonton Alb., Canada T6G 2G1 |
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Abstract: | A distance for mixed nominal, ordinal and continuous data is developed by applying the Kullback-Leibler divergence to the general mixed-data model, an extension of the general location model that allows for ordinal variables to be incorporated in the model. The distance obtained can be considered as a generalization of the Mahalanobis distance to data with a mixture of nominal, ordinal and continuous variables. Moreover, it includes as special cases previous Mahalanobis-type distances developed by Bedrick et al. (Biometrics 56 (2000) 394) and Bar-Hen and Daudin (J. Multivariate Anal. 53 (1995) 332). Asymptotic results regarding the maximum likelihood estimator of the distance are discussed. The results of a simulation study on the level and power of the tests are reported and a real-data example illustrates the method. |
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Keywords: | 62E20 62H12 62F12 |
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