On the Inference of the Population Stability Index

Thomas M. Menino Convention & Exhibition Center 

The Population Stability Index (PSI) is a widely used measure for detecting distributional changes in applications such as finance and machine learning, yet its statistical properties in particular between two continuous distributions remain largely unexplored. In this work, we study inference for PSI between two absolutely continuous distributions based on independent samples. By expressing PSI as a symmetrized Kullback–Leibler divergence, we reduce the problem to the estimation of differential entropy and cross-entropy. We construct three classes of PSI estimators derived from k-nearest neighbor, histogram, and kernel density entropy estimators. For each estimator, we investigate large-sample properties, including consistency and asymptotic distribution, under suitable regularity conditions. These results enable formal hypothesis testing for distributional equality and provide a theoretical foundation for detecting concept shift. We further discuss the asymptotic relative efficiency of the proposed estimators and offer practical recommendations for their use.

Population Stability Index

Divergence

Hypothesis Testing

Concept Drift

Model Monitoring 

Business and Economic Statistics Section