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Liquidity Risk and Financial Competition: A Mixed Integer Programming Model for Multiple-Class Discriminant Analysis

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Abstract

A mixed integer programming model is proposed for multiple-class discriminant and classificationanalysis. When multiple discriminant functions, one for each class, are constructed with the mixed integerprogramming model, the number of misclassified observations in the sample is minimized. Although having its ownright, this model may be considered as a generalization of mixed integerprogramming formulations for two-classclassification analysis. Properties of the model are studied. The model is immune from any difficulties of manymathematical programming formulations for two-class classification analysis, such as nonexistence of optimalsolutions, improper solutions and instability under linear data transformation. In addition, meaningful discriminant functions can be generated under conditions other techniques fail. Results on data sets from the literature and on data sets randomly generated show that this model is very effective in generating powerful discriminant functions.

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