Reject Inference of Incomplete Data Using a Normal Mixture Model

Abstract

Reject inference in credit scoring is a statistical approach to adjust for nonrandom sample bias due to rejected applicants. Function estimation approaches are based on the assumption that rejected applicants are not necessary to be included in the estimation,when the missing data mechanism is missing at random. On the other hand, the density estimation approach by using mixture models indicates that reject inference should include rejected applicants in the model. When mixture models are chosen for reject inference,it is often assumed that data follow a normal distribution. If data include missing values,an application of the normal mixture model to fully observed cases may cause another sample bias due to missing values. We extend reject inference by a multivariate normal mixture model to handle incomplete characteristic variables. A simulation study shows that inclusion of incomplete characteristic variables outperforms the function estimation approaches.