資料包絡分析模型在二群體區別分析之應用

The Data Envelopment Analysis Models for the Application of Two-Group Discriminant Ananlysis

郭怡君(Yi-chun Kuo)

指導教授 ： 張東生

國立中央大學/管理學院/企業管理學系/博士(2007年)

摘要

二群體的區別分析在商管領域的應用相當廣，例如破產預測、信用風險評估、顧客分析與分類、生產品質管控…。過去的文獻中有許多相關區別工具的發展，且各有其優缺點及限制。本研究將無母數之資料包絡分析模型應用於二群體的區別分析，藉由資料的處理及模型的應用，提高二群體分類的績效。本研究有三個目的，ㄧ是利用資料包絡分析法求出的包絡線去定義二群體的邊界及重疊區，由於重疊區是誤判的主要來源，若能找出最小的重疊區域及其邊界，有利於決策風險的最小化。

其二，利用層別化資料包絡分析模型求出二群體各層包絡線以及相對的生產可能集，並利用對稱剝層法消除二群體的重疊區，亦即找出能使二生產可能集為空集合的包絡線，此即為本研究定義之區別線。有別於其他方法僅有一區別線，本研究利用二群體的邊界作為區別線，其好處是不需事先假設區別函數的型態。此外本研究將建立區別規則，並利用資料包絡分析所求得之效率值作為區別指標。

其三，此部分研究將利用前二部份所建立的程序及規則去做破產預測，由於破產預測是典型的二群體樣本數不相同的型態，而且型ㄧ誤差(將健全的公司誤判為破產)及型二誤差(將破產的公司誤判為健全)的誤判風險及誤判成本皆不相同。大部分以hit-ratio為績效指標的區別分析工具會傾向高估樣本數較大的群體之正確判斷率，然而當型二誤差之誤判成本比型ㄧ誤差高出很多時，此結果會升高總誤判成本。因此，此部份研究將修正第二部份的對稱剝層法，以非對稱層別法所求得之可能誤判風險及誤判成本去計算能使總誤判成本最小化之包絡線以作為區別線。

關鍵字

資料包絡分析 ； 最小化重疊區邊界 ； 誤判成本 ； 破產預測 ； 層別化包絡線

並列摘要

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.

並列關鍵字

stratified DEA frontier ； misclassification cost ； bankruptcy prediction ； minimized overlap boundary ； Data envelopment analysis

參考文獻

Altman, E.I., Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. J Finance, 23, 589-609, 1968.

Altman, E.I., Avery, R., Eisenbeis, R. and Stinkdy, J., Application of classification techniques in business, banking and finance. Contemporary Studies in Economic and Financial Analysis, 3, JAI Press, Greenwich, CT, 1981.

Altman, E.I., Marco, G.. and Varetto, F., Corporate distress diagnosis: comparisons using discriminant analysis and neural networks (the Italian experience). J Banking Finance, 18, 505-529, 1994.

Banks, W.J. and Abad, P.L., On the performance of linear programming heuristics applied on a quadratic transformation in the classification problem. Eur J Opl Res, 74, 23-28, 1994.

Bajgier, S.M. and Hill, A.V., An experimental comparison of statistical and linear programming approaches to the discriminant problem. Dec Sci, 13, 604-618, 1982.balacel, N., Multicriteria assignment method PROAFTN: Mehtodology and medical applications. Eur J Opl Res, 125, 175-183, 2000.