Abstract
Graphical modeling as a form of multivariate analysis has turned out to be a capable tool for the detection and modeling of complex dependency structures. Statistical models are related to graphs, in which variables are represented by points and associations between each two of them as lines. The usefulness of graphical modeling depends of course on finding a graphical model, which fits the data appropriately. We will investigate how existing model building strategies and estimation methods can be affected by model disturbances or outlying observations. The focus of our sensitivity analysis lies on mixed graphical models, where both discrete and continuous variables are considered.
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References
BARNETT, V. and LEWIS, T. (1994): Outliers in Statistical Data. 3rd ed. Wiley, Chichester.
BECKER, C. and GATHER, U. (1997): Outlier Identification and Robust Methods. In: G.S. Maddala and C.R. Rao (Eds.): Handbook of Statistics 15: Robust Inference. Elsevier, Amsterdam, 123–143.
BECKER, C. and GATHER, U. (1999): The Masking Breakdown Point of Multivariate Outlier Identification Rules. Journal of the American Statistical Association, 94, 947–955.
BLAUTH, A. (2002): Model Selection in Graphical Models With Special Focus on Genetic Algorithms. Logos Verlag, Berlin.
COX, D.R. and WERMUTH, N. (1996): Multivariate Dependencies. Chapman & Hall, London.
EDWARDS, D. (2000): Introduction to Graphical Modelling. 2nd ed. Springer, New York.
EDWARDS, D. and KREINER, S. (1983): The Analysis of Contingency Tables by Graphical Models. Biometrika, 70, 553–565.
FRYDENBERG, M. and EDWARDS, D. (1989): A Modified Iterative Proportional Scaling Algorithm for Estimation in Regular Exponential Families. Comp. Statist. Data Analysis, 8, 143–153.
GATHER, U., KUHNT, S. and PAWLITSCHKO, J. (2002): Outlier Regions for Various Data Structures. To appear as invited Chapter to the Volume “Emerging Areas in Probability, Statistics and Operations Research”, Mathematical Sciences Series.
KRZANOWSKI, W.J. (1975): Discrimination and Classification Using Both Binary and Continuous Variables. Journal of the American Statistical Association, 70(352), 782–790.
KUHNT, S. (2002): Outlier Identification Procedures for Contingency Tables using Maximum Likelihood and L 1 Estimates. Submitted.
LAURITZEN, S.L. (1996): Graphical Models. Clarendon Press, Oxford.
LAURITZEN, S.L. and WERMUTH, N. (1989): Graphical Models for Associations Between Variables, Some of Which are Qualitative and Some Quantitative. Annals of Statistics, 17, 31–54.
RONCHETTI, E.M. (1997): Robustness Aspects of Model Choice. Statistica Sinica 1, 327–338.
ROUSSEEUW, P.J. (1985): Multivariate Estimation With High Breakdown Point. In: W. Grossmann, G. Pflug, I. Vincze and W. Wertz (Eds.): Mathematical Statistics and Applications. Reidel, Dordrecht, 283–297.
WHITTAKER, J. (1990): Graphical Models in Applied Mathematical Multivariate Statistics. Wiley, Chichester.
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Kuhnt, S., Becker, C. (2003). Sensitivity of Graphical Modeling Against Contamination. In: Schader, M., Gaul, W., Vichi, M. (eds) Between Data Science and Applied Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18991-3_32
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DOI: https://doi.org/10.1007/978-3-642-18991-3_32
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