| Summary: | 博士 === 國立中央大學 === 企業管理研究所 === 95 === Discriminant analysis for two-group problem has wide applicability in business environments, such as business failure prediction, credit risk assessment, analysis of the characteristics of different groups of customers and quality control of production system.
In this dissertation, a nonparametric approach based on the Data Envelopment Analysis (DEA) models is proposed to establish a pair of piecewise discriminant hyperplanes to solve the two-group discriminant problem. The dissertation includes three parts. First part of this study is to identify a minimized overlap boundary of two groups which is a major source of misclassification in discriminant problem. While the overlap boundary can be identified, the decision maker can pay more attention to the new observation which is predicted to appear within the boundary.
Second part of this study is to propose a novel procedure based on the stratified DEA model for two-group discriminant problems. Differing to most existing discriminant approaches which establish a single hyperplane for classification, a pair of nonlinear discriminant frontiers was constructed by the benchmarks of two groups. The major merit of this novel procedure is that, such nonlinear discriminant frontiers are formed by the benchmarks without the need of pre-specifying the classification function form as other parametric DA approaches do. The efficiency score is then used to be as the measurement for classification and prediction.
In the third part of this study, the methods and procedures introduced in part one and part two are applied for the application of bankruptcy prediction. In this part, we incorporate the consideration of risk and cost of TypeⅠ and Type Ⅱ errors to minimize the misclassification cost, which is usually ignored in some approaches using hit-ratio as the indicator of correct classification. Especially in an uneven case, the rule of most approaches tends to have upward biases towards the larger class (the non-bankrupt class) to increase the hit-ratio. Therefore, an asymmetric-stratified DEA model was proposed to deal with the problem while the cost of Type Ⅱ error is substantially greater than Type Ⅰ, because a little sacrifice in hit-ratio of the smaller case (bankrupt) will greatly increase the total misclassification cost.
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