Effects of User Correlation on Sample Size Requirements

摘要

Very little work has been done in determining the number of users needed to establish confidence intervals for an error rate of a biometric authentication system. The independence assumption between multiple acquisitions of an individual is too restrictive and is generally not valid. We relax this assumption and present a semi-parametric approach for estimating the within-user correlation using multivariate Gaussian copula models. We describe how to obtain confidence bands for the ROC and present the minimum requirements on the number of users needed to achieve a desired width for the ROC confidence band. Rules of thumb such as the Rule of 3 and the Rule of 30 grossly underestimate the number of users required. The underestimation becomes more severe when the correlation between any two acquisitions increases.