Kolmogorov-Smirnov Statistic Based Model Selection for Credit Scoring
王旭拓 1卫雨婷 1张焕焕2
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作者信息
1. 中国科学技术大学管理学院统计与金融系,安徽合肥 230026
2. 中国信息通信研究院,北京 100191
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摘要
信用评分系统在商业,金融,工程和健康等许多领域具有重要意义.Kolmogorov-Smirnov(KS)统计量是一种常用的评估信用评分模型的指标,Directly Maximizes the Kolmogorov-Smirnov(DMKS)是一种首次将KS统计量作为目标函数进行优化的信用评分方法.本文提出了一种基于DMKS信用评分方法以及交叉验证的模型选择方法,用于选择具有合适特征的信用评分模型,并且证明了该模型选择方法在理论上具有渐近最优性.本文使用Iterative Marginal Optimization(IMO)算法加速了模型选择准则的计算,使得本文所提模型选择方法可以适用于样本量较大的情形;同时利用前向变量选择方法的思想进一步地减少了本文所提模型选择方法的计算,从而加快了选取具有合适特征的信用评分模型的速度.模拟数据和实际数据分析表明了所提模型选择方法的有效性.
Abstract
Credit scoring plays a critical role in many areas such as business,finance,engineering and health.The Kolmogorov-Smirnov statistic is a commonly used criterion for evaluating scoring method's performance.Directly Maximizes the Kolmogorov-Smirnov(DMKS)is a credit scoring method that optimizes KS statistic as an objective function for the first time.In this paper,based on DMKS and cross-validation,we develop a new model selection method for choosing a suitable credit scoring model.We further prove the asymptotic optimality of our proposed method.Iterative Marginal Optimization(IMO)algorithm is used to accelerate the calculation of the proposed model selection criterion,so that our proposal can be applied when the sample size is large.In addition,the calculation of our proposed model selection method is further reduced by using the idea of the forward variable selection method,and thus the speed of selecting a suitable credit scoring model is accelerated.Simulation studies and a real data analysis show the effectiveness of the proposed model selection method.
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