Optimal Threshold from AROC Curve

• Activity Number: 516
• Type: Contributed
• Date/Time: Wednesday, August 4, 2010 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Chong Sun Hong+ and Jin Soo Choi* and Hee Jeong Lee
• Companies: SKK University and SKK University and SKK University
• Keywords: credit ; discriminatory ; default ; odds-ratio ; score

Abstract

Assuming a mixture distribution for credit evaluation studies with the score random variable, ROC curve is a useful plot to access the discriminatory power of different credit-rating approaches. Even though any point on ROC curve is represented as some functions of a certain score, the score corresponding to each point on ROC curve cannot be obtained. We propose an alternative curve whose horizontal axis is the score, called as Adjusted ROC (AROC) curve. This AROC curve has an advantage that it can be identified with every score. Some shapes of AROC curves are explored based on mixtures of two distributions. By using methods of finding optimal threshold, the relationship of AROC curve is identified. An optimal threshold could be estimated based on the local minimum of the AROC curve, when the variances of two distributions are identical.