A new approach for credit scoring by directly maximizing the Kolmogorov–Smirnov statistic

Credit scoring plays a critical role in many areas such as business, finance, engineering and health. The Kolmogorov–Smirnov statistic is one of the most important performance evaluation criteria for scoring methods and has been widely used in practice. However, none of the existing scoring methods deals with the Kolmogorov–Smirnov statistic directly at the modeling stage. To fill the gap, a new credit scoring method that Directly Maximizes the Kolmogorov-Smirnov statistic (DMKS) is proposed. Theoretically, the consistency of the proposed DMKS estimator is proved. Computationally, an iterative marginal optimization algorithm and a smoothed pool-adjacent-violators algorithm are proposed to overcome the computational difficulties caused by the neither smooth nor continuous objective function. Empirically, results of simulation studies and two real business examples are presented. The proposed method compares favorably with the popular existing scoring methods considering the tradeoff among predictive ability in terms of KS, computational complexity and practical interpretability.